1.An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?
24
2. How many permutations of three items can be selected from a group of six?
120
BDF BFD DBF DFB FBD FDB
3. A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: , , , and . Are these probability assignments valid? Explain.
No, they are greater than or equal to 0, but do not sum to 1.
4. A CBS News/New York Times poll of adults in the United States asked the question, “Do you think global warming will have an impact on you during your lifetime?” (CBS News website). Consider the responses by age groups shown below.
a. What is the probability that a respondent – years of age thinks that global warming will not have an impact during his/her lifetime (to decimals)?
0.4906
b. What is the probability that a respondent + years of age thinks that global warming will not have an impact during his/her lifetime (to decimals)?
0.5894
c. For a randomly selected respondent, what is the probability that a respondent answers yes (to decimals)?
0.427
d. Based on the survey results, does there appear to be a difference between ages – and + regarding concern over global warming?
It appears that older respondents are less concerned about global warming being a threat in their lifetime than are younger respondents.
4. The National Highway Traffic Safety Administration (NHTSA) collects traffic safety-related data for the U.S. Department of Transportation. According to NHTSA’s data, fatal collisions in were the result of collisions with fixed objects (NHTSA website, https://www.careforcrashvictims.com/wp-content/uploads/2018/07/Traffic-Safety-Facts-2016_-Motor-Vehicle-Crash-Data-from-the-Fatality-Analysis-Reporting-System-FARS-and-the-General-Estimates-System-GES.pdf). The following table provides more information on these collisions.
| Fixed Object Involved in Collision | Number of Collisions | |
| Pole/post | 1,416 | |
| Culvert/curb/ditch | 2,516 | |
| Shrubbery/tree | 2,585 | |
| Guardrail | 896 | |
| Embankment | 947 | |
| Bridge | 231 | |
| Other/unknown | 1,835 | |
a. What is the probability of a fatal collision with a pole or post?
0.1358
b. What is the probability of a fatal collision with a guardrail?
0.0859
c. What type of fixed object is least likely to be involved in a fatal collision?
Bridge
What is the probability associated with this type of fatal collision?
0.0222
d. What type of object is most likely to be involved in a fatal collision?
Shrubbery/tree
What is the probability associated with this type of fatal collision?
0.2479
5. A Pew Research Center survey (Pew Research website) examined the use of social media platforms in the United States. The survey found that there is a probability that a randomly selected American will use Facebook and a probability that a randomly selected American will use LinkedIn. In addition, there is a probability that a randomly selected American will use both Facebook and LinkedIn.
a. What is the probability that a randomly selected person will use Facebook or LinkedIn (to decimals)?
0.71
b. What is the probability that a randomly selected person will not use either social media platform (to decimals)?
0.29
6. High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admissions class, an Ivy League college received applications for early admission. Of this group, it admitted students early, rejected outright, and deferred to the regular admissions pool for further consideration. In the past, this school has admitted of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was . Let , , and represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.
a. Use the data to estimate , , and (to decimals).
0.362329
0.299544
0.338127
b. Are events and mutually exclusive?
Yes, they are mutually exclusive.
Find (to decimals).
0
c. For the students who were admitted, what is the probability that a randomly selected student was accepted for early admission (to decimals)?
0.4349
d. Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process (to decimals)?
0.4232
7. Assume that we have two events, and , that are mutually exclusive. Assume further that we know and .
a. What is ?
0
b. What is ?
0
c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.
No Not equal to
d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
Mutually exclusive events are dependent.
8. To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of married adults age and older with household incomes of or more (Money website). Consider the following example set of responses to the question, “Who is better at getting deals?”
| Who Is Better? | |||
| Respondent | I Am | My Spouse | We Are Equal |
| Husband | 278 | 127 | 102 |
| Wife | 290 | 111 | 102 |
a. Develop a joint probability table and use it to answer the following questions.
Husband 0.275248 0.12574257 0.101 0.502
Wife 0.287 0.110 0.101 0.498
Total 0.5624 0.2356 0.202 1.000
b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.
The probability of “I Am” 0.5624
The probability of “My Spouse 0.2356
The probability of “We Are Equal” 0.2020
I am My spouse or We are equal
c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife?
0.548323
d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?
0.576541
e. Given a response “My spouse” is better at getting deals, what is the probability that the response came from a husband?
0.533613
f. Given a response “We are equal,” what is the probability that the response came from a husband?
0.5
What is the probability that the response came from a wife?
0.5
9. A Pew Research Center survey found that more Americans believe they could give up their televisions than could give up their cell phones (Pew Research website). Assume that the following table represents the joint probabilities of Americans who could give up their television or cell phone.
a. What is the probability that a person could give up her cell phone (to decimals)?
0.48
b. What is the probability that a person who could give up her cell phone could also give up television (to decimals)?
0.65
c. What is the probability that a person who could not give up her cell phone could give up television (to decimals)?
0.73
d. Is the probability a person could give up television higher if the person could not give up a cell phone or if the person could give up a cell phone?
Higher
10. A consulting firm submitted a bid for a large research project. The firm’s management initially felt they had a chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for of the successful bids and of the unsuccessful bids the agency requested additional information.
a. What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to decimal)?
0.5
b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to decimals)?
0.72
c. Compute the posterior probability that the bid will be successful given a request for additional information (to decimals).
0.66
11. According to a article in Esquire magazine, approximately of males over age will develop cancerous cells in their prostate. Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSA) test. However, this test is known to have a high false-positive rate (tests that come back positive for cancer when no cancer is present). Suppose there is a probability that a male patient has prostate cancer before testing. The probability of a false-positive test is , and the probability of a false-negative (no indication of cancer when cancer is actually present) is .
a. What is the probability that the male patient has prostate cancer if the PSA test comes back positive (to decimals)?
0.0213
b. What is the probability that the male patient has prostate cancer if the PSA test comes back negative (to decimals)?
0.0161
c. For older men, the prior probability of having cancer increases. Suppose that the prior probability of the male patient is rather than . What is the probability that the male patient has prostate cancer if the PSA test comes back positive (to decimals)?
0.3137
What is the probability that the male patient has prostate cancer if the PSA test comes back negative (to decimals)?
0.2553
d. What can you infer about the PSA test from the results of parts (a), (b), and (c)?
Lower
12. A financial manager made two new investments—one in the oil industry and one in municipal bonds. After a one-year period, each of the investments will be classified as either successful or unsuccessful. Consider the making of the two investments as an experiment.
a. How many sample points exist for this experiment?
4
b. Choose a tree diagram.
c
c. Let and
How many sample points exist for ?
2
How many sample points exist for ?
2
d. Identify the sample points in the union of the events ().
E1,E2,E3
e. Identify the sample points in the intersection of the events ().
E1
f. Are events and mutually exclusive? Explain.
No, because of E1
13. A study of hospital admissions in New York State found that of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of cases involving negligence, and payments were made in one out of every two claims.
a. What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence (to decimals)?
0.01
b. What is the probability a person admitted to the hospital will die from a treatmen-caused injury (to decimals)?
0.006
c. What is the probability a person admitted to the hospital is paid a malpractice claim (to decimals)?
0.00067
14. A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events.
B = individual purchased the product
S = individual recalls seeing the advertisement
B ∩ S = individual purchased the product and recalls seeing the advertisement
The probabilities assigned were , , and
a. What is the probability of an individual’s purchasing the product given that the individual recalls seeing the advertisement (to decimal)?
0.3
Does seeing the advertisement increase the probability that the individual will purchase the product?
‘Yes, seeing the advertisement increases the probability of purchase.
As a decision maker, would you recommend continuing the advertisement (assuming that the cost is reasonable)?
Yes, continue the advertisement.
b. Assume that individuals who do not purchase the company’s soap product buy from its competitors. What would be your estimate of the company’s market share (to the nearest whole number)?
20.
Would you expect that continuing the advertisement will increase the company’s market share? Why or why not?
Yes, because P(BIS) is greater than P(B).
c. The company also tested another advertisement and assigned it values of and . What is for this other advertisement (to decimals)?
0.333
Which advertisement seems to have had the bigger effect on customer purchases?
The second ad has a bigger effect.
15. A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to during the current year. In addition, it estimates that of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years (to decimals)?
1.35
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period (to decimals)?
15.65
16. An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
a. What is the probability of finding oil (to decimals)?
0.65
b. After feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below.
Given the soil found in the test, use Bayes’ theorem to compute the following revised probabilities (to decimals).
0.2941
0.5000
0.2059
What is the new probability of finding oil (to decimals)?
0.7941
According to the revised probabilities, what is the quality of oil that is most likely to be found?
Medium-quality
16. To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.
a. List the experimental outcomes associated with performing the blood analysis.
1,1), (1,2), (1,3), (2,1), (2,2), (2, 3)
b. Let denote the total number of steps required to do the complete analysis (both procedures). Show what value of random variable will assume for each of the experimental outcomes. (If an outcome does not occur, enter “0”.)
0
0
0
2
3
4
3
4
5
0
0
0
17. A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take , , , or hours. The different types of malfunctions occur at the same frequency.
a. Develop a probability distribution for the duration of a service call.
0.25
0.25
0.25
0.25
1
b. Which of the following probability distribution graphs accurately represents the data set?
Probability distribution #2
c. Consider the required conditions for a discrete probability function, shown below.
Yes, all probability function values are greater than or equal to 0.
Does this probability distribution satisfy equation (5.2)?
Yes, the sum of all probability function values equals 1.
d. What is the probability a service call will take hours?
0.25
e. A service call has just come in, but the type of malfunction is unknown. It is P.M. and service technicians usually get off at P.M. What is the probability the service technician will have to work overtime to fix the machine today?
0.5
18. A psychologist determined that the number of sessions required to obtain the trust of a new patient is either , , or . Let be a random variable indicating the number of sessions required to gain the patient’s trust. The following probability function has been proposed.
a. Consider the required conditions for a discrete probability function, shown below.
Yes, all probability function values are greater than or equal to 0
Does this probability distribution satisfy equation (5.2)?
‘Yes, the sum of all probability function values equals 1
b. What is the probability that it takes exactly sessions to gain the patient’s trust (to 3 decimals)?
0.333
c. What is the probability that it takes at least sessions to gain the patient’s trust (to 3 decimals)?
0.833
19. The following table provides a probability distribution for the random variable .
a. Compute , the expected value of .
6
b. Compute 2, the variance of (to 1 decimal).
4.5
c. Compute , the standard deviation of (to 2 decimals).
2.12
20. New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond. These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backen and Hayes LLC is an accounting firm in New York state. The accounting firm believes that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming tax season. Backen and Hayes LLC has developed the following probability distribution for number of new clients seeking tax advice.
a. Is this a valid probability distribution?
Yes
Greater than or equal to
equal to
b. What is the probability that Backen and Hayes LLC will obtain or more new clients (to 2 decimals)?
0.35
c. What is the probability that Backen and Hayes LLC will obtain fewer than new clients (to 2 decimals)?
0.50
d. Compute the expected value, variance, and standard deviation of (to 2 decimals).
34.25
73.1875
8.554969
21. The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of (very dissatisfied) to a high of (very satisfied).
a. What is the expected value of the job satisfaction score for senior executives (to 2 decimals)?
4.05
b. What is the expected value of the job satisfaction score for middle managers (to 2 decimals)?
3.84
c. Compute the variance of job satisfaction scores for executives and middle managers (to 2 decimals).
1.25
1.13
d. Compute the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals).
1.12
1.06
e. What comparison can you make about the job satisfaction of senior executives and middle managers?
Senior executives have higher satisfaction with more variation
22. J. P. Morgan Asset Management publishes information about financial investments. Between 2002 and 2011 the expected return for the S&P was with a standard deviation of and the expected return over that same period for a Core Bonds fund was with a standard deviation of (J. P. Morgan Asset Management, Guide to the Markets). The publication also reported that the correlation between the S&P and Core Bonds is . You are considering portfolio investments that are composed of an S&P index fund and a Core Bonds fund.
a. Using the information provided, determine the covariance between the S&P and Core Bonds. Round your answer to two decimal places. If required enter negative values as negative numbers.
-13.26
b. Construct a portfolio that is invested in an S&P index fund and in a Core Bond fund. Let x represent the S&P 500 and y represent the Core Bond fund. Round your answers to one decimal place.
0.5 0.5
In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.
5.41
9.44
c. Construct a portfolio that is invested in an S&P index fund and invested in a Core bond fund. Let x represent the S&P 500 and y represent the Core Bond fund. Round your answers to one decimal place.
0.2 0.8
In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.
5.63
3.71
d. Construct a portfolio that is invested in an S&P index fund and invested in a Core bond fund. Let x represent the S&P 500 and y represent the Core Bond fund. Round your answers to one decimal place.
0.8 0.2
In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.
5.19
15.43
e. Which of the portfolios in parts (b), (c), and (d) above has the largest expected return?
part c
part c
part c
part d
part c
23. Consider a binomial experiment with and .
a. Compute (to 4 decimals).
0.1144
b. Compute (to 4 decimals).
0.1304
c. Compute (to 4 decimals).
0.2374
d. Compute (to 4 decimals).
0.7626
e. Compute .
14
f. Compute (to 1 decimal) and (to 2 decimals).
4.2
2.05
24. The Center for Medicare and Medical Services reported that there were appeals for hospitalization and other Part A Medicare service. For this group, of first round appeals were successful (The Wall Street Journal). Suppose first-round appeals have just been received by a Medicare appeals office. Refer to Binomial Probability Table.
a. Compute the probability that none of the appeals will be successful.
0.006
b. Compute the probability that exactly one of the appeals will be successful.
0.0403
c. What is the probability that at least two of the appeals will be successful?
0.9537
d. What is the probability that more than half of the appeals will be successful?
0.1662
25. Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of , Google’s Chrome browser exceeded a market share for the first time, with a share of the browser market (Forbes website). For a randomly selected group of Internet browser users, answer the following questions.
a. Compute the probability that exactly of the Internet browser users use Chrome as their Internet browser (to 4 decimals). For this question, if you compute the probability manually, make sure to carry at least six decimal digits in your calculations.
0.0243
b. Compute the probability that at least of the Internet browser users use Chrome as their Internet browser (to 4 decimals).
0.8050
c. For the sample of Internet browser users, compute the expected number of Chrome users (to 3 decimals).
4.074
d. For the sample of Internet browser users, compute the variance and standard deviation for the number of Chrome users (to 3 decimals).
3.2441
1.8011
26. A university found that of its students withdraw without completing the introductory statistics course. Assume that students registered for the course.
a. Compute the probability that or fewer will withdraw (to 4 decimals).
0.0355
b. Compute the probability that exactly will withdraw (to 4 decimals).
0.1304
c. Compute the probability that more than will withdraw (to 4 decimals).
0.8930
d. Compute the expected number of withdrawals.
6
27. According to a Wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (Wired magazine website). Suppose we randomly select received e-mails.
a. What is the expected number of these e-mails that are tracked?
20
b. What are the variance (to the nearest whole number) and standard deviation (to 3 decimals) for the number of these e-mails that are tracked?
12
3.464
28. Emergency calls to a small municipality in Idaho come in at the rate of one every minutes.
a. What is the expected number of calls in one hour?
30
b. What is the probability of three calls in five minutes (to 4 decimals)?
0.2138
c. What is the probability of no calls in a five-minute period (to 4 decimals)?
0.0821
29. Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is passengers per minute.
a. Compute the probability of no arrivals in a one-minute period (to 6 decimals).
0.000336
b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals).
0.0424
c. Compute the probability of no arrivals in a -second period (to 4 decimals).
0.1354
d. Compute the probability of at least one arrival in a -second period (to 4 decimals).
0.8646
30. According to a survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a. What is the probability of receiving no e-mails during an hour (to 4 decimals)?
0.0067
b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.
0.8753
c. What is the expected number of e-mails received during minutes (to 2 decimals)?
1.25
d. What is the probability that no e-mails are received during minutes (to 4 decimals)?
0.2865
31. Suppose and .
What is the probability of for (to 4 decimals)?
0.4396
32. The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For restaurants located in Boston, the average price of a dinner, including one drink and tip, was . You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed . Suppose that you randomly select three of these restaurants for dinner.
a. What is the probability that none of the meals will exceed the cost covered by your company (to 4 decimals)?
0.2637
b. What is the probability that one of the meals will exceed the cost covered by your company (to 4 decimals)?
0.4945
c. What is the probability that two of the meals will exceed the cost covered by your company (to 4 decimals)?
0.2198
d. What is the probability that all three of the meals will exceed the cost covered by your company (to 4 decimals)?
0.0220
33. Delta Airlines quotes a flight time of hours, minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between hours and hours, minutes.
Graph #1
b. What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)?
0.5
c. What is the probability that the flight will be more than 10 minutes late (to 2 decimals)?
0.25
d. What is the expected flight time, in minutes?
130
34. The electric-vehicle manufacturing company Tesla estimates that a driver who commutes miles per day in a Model S will require a nightly charge time of around hour and minutes ( minutes) to recharge the vehicle’s battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between and minutes.
a. Give a mathematical expression for the probability density function of battery recharging time for this scenario.
A
b. What is the probability that the recharge time will be less than minutes (to 3 decimals)?
0.666
c. What is the probability that the recharge time required is at least minutes (to 3 decimals)?
0.666
d. What is the probability that the recharge time required is between and minutes (to 3 decimals)?
0.5
35. Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of will be accepted. Assume that the competitor’s bid is a random variable that is uniformly distributed between and .
a. Suppose you bid . What is the probability that your bid will be accepted (to 2 decimals)?
0.50
b. Suppose you bid . What is the probability that your bid will be accepted (to 2 decimals)?
0.90
c. What amount should you bid to maximize the probability that you get the property?
14500
d. Suppose that you know someone is willing to pay you for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid . Which bid will give you the larger expected profit?
Bid $12750 to maximize the expected profit
What is the expected profit for this bid (to 2 decimals)?
2112.50
36. A random variable is normally distributed with a mean of and a standard deviation of .
a. Which of the following graphs accurately represents the probability density function?
A
b. What is the probability that the random variable will assume a value between and (to 4 decimals)?
0.6826
c. What is the probability that the random variable will assume a value between and (to 4 decimals)?
0.9544
37. Given that is a standard normal random variable, compute the following probabilities (to 4 decimals).
0.1587
0.8413
0.9332
0.9938
0.4987
38. Males in the Netherlands are the tallest, on average, in the world with an average height of centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of cm and standard deviation of cm.
a. What is the probability that a Dutch male is shorter than cm (to 4 decimals)?
0.2236
b. What is the probability that a Dutch male is taller than cm (to 4 decimals)?
0.1271
c. What is the probability that a Dutch male is between and cm (to 4 decimals)?
0.6578
d. Out of a random sample of Dutch men, how many would we expect to be taller than cm (rounded to the nearest whole number)?
252
39. A person must score in the upper of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of and a standard deviation of , what score must a person have to qualify for Mensa (to whole number)?
131
40. The time needed to complete a final examination in a particular college course is normally distributed with a mean of minutes and a standard deviation of minutes. Answer the following questions.
a. What is the probability of completing the exam in one hour or less (to 4 decimals)?
0.0384
b. What is the probability that a student will complete the exam in more than minutes but less than minutes (to 4 decimals)?
0.2307
c. Assume that the class has students and that the examination period is minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to nearest whole number)?
18
41. According to Money magazine, Maryland had the highest median annual household income of any state in at (Time.com website). Assume that annual household income in Maryland follows a normal distribution with a median of and standard deviation of .
a. What is the probability that a household in Maryland has an annual income of or more (to 4 decimals)?
0.2389
b. What is the probability that a household in Maryland has an annual income of or less (to 4 decimals)?
0.1446
c. What is the probability that a household in Maryland has an annual income between and (to 4 decimals)?
0.2089
d. What is the annual income of a household in the percentile of annual household income in Maryland (to the nearest dollar)?
119111
42. Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In , the Amazon Alexa app was downloaded some times per day from the Google Play store (AppBrain website). Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of and standard deviation of .
a. What is the probability there are or fewer downloads of Amazon Alexa in a day (to 4 decimals)?
0.1762
b. What is the probability there are between and downloads of Amazon Alexa in a day (to 4 decimals)?
0.2977
c. What is the probability there are more than downloads of Amazon Alexa in a day (to 4 decimals)?
0.4090
d. Assume that Google has designed its servers so there is probability that the number of Amazon Alexa app downloads in a day exceeds the servers’ capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google’s servers designed to handle (to the nearest whole number)?
4800
43. The XO Group Inc. conducted a survey of brides and grooms married in the United States and found that the average cost of a wedding is (XO Group website). Assume that the cost of a wedding is normally distributed with a mean of and a standard deviation of .
a. What is the probability that a wedding costs less than (to 4 decimals)?
0.0392
b. What is the probability that a wedding costs between and (to 4 decimals)?
0.4728
c. For a wedding to be among the most expensive, how much would it have to cost (to the nearest whole number)?
39070
44. According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health sciences was . The average starting salary for new college graduates in business was (National Association of Colleges and Employers website). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is . Assume that the standard deviation for starting salaries for new college graduates in business is .
a. What is the probability that a new college graduate in business will earn a starting salary of at least (to 4 decimals)?
0.2296
b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least (to 4 decimals)?
0.1112
c. What is the probability that a new college graduate in health sciences will earn a starting salary less than (to 4 decimals)?
0.1469
d. How much would a new college graduate in business have to earn in order to have a starting salary higher than of all starting salaries of new college graduates in the health sciences (to the nearest whole number)?
77171.00
45. Do you dislike waiting in line? Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at stores. Using a new system called QueVision, which allows Kroger to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just seconds (InformationWeek website). Assume that waiting times at Kroger are exponentially distributed.
a. Which of the probability density functions of waiting time is applicable at Kroger?
B
b. What is the probability that a customer will have to wait between and seconds (to 4 decimals)?
0.2462
c. What is the probability that a customer will have to wait more than minutes (to 4 decimals)?
0.0099
46. Consider the following exponential probability density function.
a. Which of the following is the formula for ?
Formula #2
b. Find (to 4 decimals).
0.4867
c. Find (to 4 decimals).
0.2635
d. Find (to 4 decimals).
0.8647
e. Find (to 4 decimals).
0.3781
47. Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. According to a large-scale study of elderly ICU patients, the average length of stay in the ICU is days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations.
a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)?
0.2549
b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)?
0.1415
c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?
0.2297
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