Question 1

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. What is the standard deviation of the temperature increase?
A) 10.12
B) 4.33
C) 7.50
D) 1.25

Accepted Answer

=== 4.33

Question 2

Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean?
A) .75
B) 1.00
C) .58
D) .86

Accepted Answer

M = (65 + 40)/2 = 52.5
σ == 7.22
P(μ − 2σ ≤ x ≤ μ + 2σ) = P(38.1 ≤ x ≤ 66.9) = 1

Question 3

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Ninety-nine percent of the households spent less than what amount?
A) $5.66
B) $10.78
C) $6.81
D) $9.63

Accepted Answer

z_.99 = 2.33 = (x − 8.22)/1.10 x = 2.563 + 8.22 = $10.78

Question 4

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. What proportion of the households spent between $5.00 and $9.00 on sugar?
A) .7611
B) .7628
C) .0017
D) .7592

Accepted Answer

P(5 < X < 9) = p= p= p(−2.93 < x < .71)
= .7609 − .0017 = .7592

Question 5

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. What is the expected value of the temperature increase?
A) 7.50
B) 4.33
C) 17.50
D) 10.12

Accepted Answer

= 17.5

Question 6

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. Only 5 percent of the students taking the test scored higher than what grade?
A) 70.04
B) 67.96
C) 55.48
D) 83.81

Accepted Answer

z_.95= 1.645 = (x − 69)/9 x = 83.81

Question 7

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent more than $10.00 on sugar.
A) .7320
B) .9474
C) .0528
D) .2680

Accepted Answer

P(x > 10) = p= 1.000 − .9472 = .0528

Question 8

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. In an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?
A) 34.48
B) 21.68
C) 38.32
D) 25.52

Accepted Answer

z_.85 = 1.04 = (x − 30)/8; x = 38.32

Question 9

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Complete the following statement: Only 20 percent of the individuals wait less than ________ minutes.
A) 36.72
B) 23.28
C) 34.63
D) 25.37

Accepted Answer

z_.20 = −.84 = (x − 30)/8 = −6.72 + 30 x = 23.28

Question 10

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent more than $16.00 on sugar.
A) 1.00
B) .00
C) .50
D) .98

Accepted Answer

P(x > 16) = p= p(z > 7.07)

Question 11

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent less than $5.00 on sugar.
A) .9983
B) .000
C) 1.00
D) .0017

Accepted Answer

P(x < 5.00) = p= p(z < −2.93) = .0017

Question 12

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What percentage of students scored between 65 and 89?
A) 65.85%
B) 100%
C) 98.68%
D) 33.00%

Accepted Answer

P(65 ≤ x ≤ 89) = p= p(−.44 ≤ z ≤ 2.22)
= .9869 − .3284 = .6585

Question 13

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time of at least 10 minutes?
A) .9938
B) .8944
C) .1056
D) .0062

Accepted Answer

P(x ≥ 10) = p= p(z ≥ −2.5) = 1.0 − .0062 = .9938

Question 14

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes?
A) 1.00
B) .9699
C) .5000
D) .9392

Accepted Answer

P(15 ≤ x ≤ 45) = P(−1.875 ≤ z ≤ 1.875) = .9696 − .0304 = .9392

Question 15

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. Suppose that a temperature increase of 18° C or more is considered to be potentially dangerous to the environment. What is the probability that at any point in time, the temperature increase is potentially dangerous?
A) .47
B) .72
C) .28
D) .50

Accepted Answer

P (x > 18) === .47

Question 16

Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit will take at least 50 minutes?
A) .77
B) .40
C) .60
D) .23

Accepted Answer

p(x > 50) === .6

Question 17

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Eighty percent of the households spent more than what amount?
A) $7.30
B) $7.38
C) $9.06
D) $9.14

Accepted Answer

z_.20 = −.84 = (x − 8.22)/1.10 x − 8.22= −.924 x = 8.22 − .924 = 7.296

Question 18

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What proportion of students scored between 81 and 89?
A) .0668
B) .0132
C) .0781
D) .0529

Accepted Answer

P(81 ≤ x ≤ 89) = P(1.3333 ≤ z ≤ 2.2222) = .9869 − .9088 = .0781

Question 19

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What is the probability of getting a grade of 91 or less on this exam?
A) 1.00
B) .50
C) .0073
D) .9927

Accepted Answer

P(x ≤ 91) = p(z ≤ [91 − 69]/9) = p(z ≤ 2.44) = .9927

Question 20

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. What is the probability that a randomly selected individual will have a waiting time of no more than 22 minutes?
A) .1587
B) .9977
C) .8413
D) .0023

Accepted Answer

P(x ≤ 22) = p= p(z < −1) = .1587

Quiz 7: Continuous Random Variables

Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean?

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Ninety-nine percent of the households spent less than what amount?

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. What proportion of the households spent between $5.00 and $9.00 on sugar?

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. Only 5 percent of the students taking the test scored higher than what grade?

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent more than $10.00 on sugar.

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent more than $16.00 on sugar.

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Find the probability that a household spent less than $5.00 on sugar.

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What percentage of students scored between 65 and 89?

Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit will take at least 50 minutes?

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Eighty percent of the households spent more than what amount?

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What proportion of students scored between 81 and 89?

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What is the probability of getting a grade of 91 or less on this exam?