1.For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is
0.945201
2.The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in 7 minutes or more is _____.
| 10 | 10 | |||||||||||||
| 6 | 7 | |||||||||||||
| 4 | 3 |
0.75
3.Assume z is a standard normal random variable. Then P(–1.96 ≤ z ≤ –1.6) equals _____.
| 1.96 | 0.024998 | ||||||||||
| -1.5 | 0.066807 |
0.041809
4.Consider the following.
f(x) = (1/19) e –x/19 x ≥ 0
The probability that x is between 7 and 9 is
| 19 | 7 | 0.308174 | ||||||||||||
| 0.05 | 9 | 0.377296 | ||||||||||||
0.069122
5.The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?
| 40000 | ||||||||||||||
| 5000 | -2 | 0.02275 | ||||||||||||
| 30000 | ||||||||||||||
0.97725,P(Z>-2
6.Consider the following.
f(x) = (1/8) e –x/8 x ≥ 0
The mean of x is _____.
8
7.Suppose x is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is _____.
| mean | 5 | 10.52 | 2.76 | 0.99711 | ||||||||
| variance | 4 |
P(Z>2.76), 0.0029
8.Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-1. The probability that x will take on a value between 21 and 25 is_____.
20 21
28 25
8 4
0.5
Exhibit 6-2
9.The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
Refer to Exhibit 6-2. The probability that she will finish her trip in 80 minutes or less is _____.
40 40
90 80
50 40
0.8
10.The travel time for a college student traveling between her home and her college is uniformly distributed between 50 and 80 minutes. The probability that she will finish her trip in 60 minutes or less is _____.
50 50
80 60
30 10
0.333333
11.Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1112?
0
0.5
12.The weight of items produced by a machine is normally distributed with a mean of 9 ounces and a standard deviation of 3 ounces. What is the probability that a randomly selected item will weigh more than 12 ounces?
mean 9
variance 3
12 1
0.841345
P(Z>2.76) 0.1587
13.The assembly time for a product is uniformly distributed between 6 and 8 minutes. The probability density function has what value in the interval between 6 and 8?
6
8
0.5
14.Consider the continuous random variable x, which has a uniform distribution over the interval from 40 to 48. The variance of x is approximately _____.
40
48 8 64
5.333333
15.The life expectancy of a particular brand of tire is normally distributed with a mean of 30,000 and a standard deviation of 6,000 miles. What percentage of tires will have a life of 21,600 to 38,400 miles
mean 30000
variance 600
21600 -1.4 0.080757
| P(Z>2.76) | 0.9192 |
Exhibit 6-5
16.The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh between 11 and 12 ounces?
mean 8
variance 2
11 1.5
0.933193
| P(Z>2.76) | 0.0668 |
mean 8
variance 2
12 2
0.97725
| P(Z>2.76) | 0.0228 | 0.9104 |
0.0441
17.Assume z is a standard normal random variable. Then P(z ≥ 2.11) equals _____.
2.11 0.982571
0.017492
Exhibit 6-7
18.f(x) = (1/10) e–x/10 x ≥ 0
Refer to Exhibit 6-7. The probability that x is between 3 and 6 is _____
10
0.10
3 0.259182
6 0.451188
0.192007
19.The assembly time for a product is uniformly distributed between 6 and 11 minutes. The probability of assembling the product in 7 to 9 minutes is _____.
6 7
11 9
5 2
0.4
Exhibit 6-4
20.The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
Refer to Exhibit 6-4. What percentage of MBAs will have starting salaries of $34,000 to $46,000?
mean 40000
variance 5000
-1.2 0.11507
34000
P(Z>2.76) 0.8849
mean 40000
variance 5000
-1.2 0.11507
46000
P(Z>2.76) 0.1151
21.Assume z is a standard normal random variable. What is the value of z if the area between –z and z is 0.8557?
0.8611
1.8611
0.93055
1.48
22.Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.9370?
P(Z<z) = 0.937
right 0.063 -1.53007
1.530068
23.The life expectancy of a particular brand of tire is normally distributed with a mean of 30,000 and a standard deviation of 6,000 miles. What is the probability that a randomly selected tire will have a life of at least 24,000 miles?
mean 30000
STD 6000
24000
-1 0.158655
P(Z>-1)
0.8413
24.The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
Refer to Exhibit 6-2. The probability that her trip will take longer than 60 minutes is _____.
40 40
90 60
50 20
0.4
25.The travel time for a college student traveling between her home and her college is uniformly distributed between 30 and 70 minutes. The probability that her trip will take longer than 50 minutes is _____.
30 30
70 50
40 20
0.5
26.Consider the following.
f(x) = (1/18) e -x/18 x ≥ 0
The probability that x is between 7 and 9 is _____.
18
0.06
7 0.32219
9 0.393469
0.071279
27.The assembly time for a product is uniformly distributed between 1 and 7 minutes. The standard deviation of assembly time (in minutes) is approximately _____.
1
7
3
28.The weight of football players is normally distributed with a mean of 215 pounds and a standard deviation of 20 pounds. What percent of players weigh between 205 and 225 pounds?
mean 215
STD 20
205
-0.5 0.308538
P(Z>2.76) 0.6915
mean 215
STD 20
225
0.5 0.691462
P(Z>2.76) 0.3085
0.3829 38.29%
0.0000
29.The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in 7 to 9 minutes is _____.
6 7
10 9
4 2
0.5
30.The weight of items produced by a machine is normally distributed with a mean of 9 ounces and a standard deviation of 2 ounces. What is the probability that a randomly selected item weighs exactly 9 ounces?
mean 9
variance 2
9
0 0.5
P(Z>2.76) 0.5000
31.The starting salaries of individuals with an MBA degree are normally distributed with a mean of $35,000 and a standard deviation of $8,000. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $43,800?
mean 35000
STD 8000
43800
1.1 0.864334
P(Z>-1) 0.1357
32.Assume z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9911?
P(Z<z) =0.0089
right 0.9911 2.369752
-2.36975
33.Suppose x is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is _____.
mean 5
STD 4
10.52
1.38 0.916207
P(Z>-1) 0.0838
34.The travel time for a college student traveling between her home and her college is uniformly distributed between 60 and 90 minutes. The probability that she will finish her trip in 80 minutes or less is _____.
60 60
90 80
30 20
0.666667
35.The weight of football players is normally distributed with a mean of 220 pounds and a standard deviation of 20 pounds. What is the minimum weight of the middle 95% of the players?
220
20
0.95
1.95
0.975 1.959964
value= 259.2
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