Chapter 5 Exercise 4
A large company must hire a new president. The Board of Directors prepares a list of five candidates, all
of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias
in the selection of the candidate, the company decides to select the president by lottery.
a. What is the probability one of the minority candidates is hired? (Round your answer to 1 decimal
place.)
Probability 0.4
b. Which concept of probability did you use to make this estimate?
Classical
Chapter 5 Exercise 14
The chair of the board of directors says, "There is a 50% chance this company will earn a profit, a 30%
chance it will break even, and a 20% chance it will lose money next quarter."
a. Use an addition rule to find the probability the company will not lose money next quarter. (Round
your answer to 2 decimal places.)
0.5 + 0.3 = 0.8
b. Use the complement rule to find the probability it will not lose money next quarter. (Round your
answer to 2 decimal places.)
1.0 - 0.2 = 0.8
Chapter 5 Exercise 22
A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit
Yellowstone Park, 40% visit the Tetons, and 35% visit both.
a. What is the probability a vacationer will visit at least one of these attractions? (Round your answer to
2 decimal places.)
Probability 0.55
b. What is the probability .35 called?
Joint
c. Are the events mutually exclusive?
No
Chapter 5 Exercise 34
P(A1) = .20, P(A2) = .40, and P(A3) = .40. P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10.
Use Bayes' theorem to determine P(A3|B1). (Round your answer to 4 decimal places.)
P(A3|B1) 0.3636
Chapter 5 Exercise 40
Solve the following:
a. 20! 17!
6,840
b. 9P3
504
c. 7C2
21
Chapter 6 Exercise 4
Which of these variables are discrete and which are continuous random variables?
a. The number of new accounts established by a salesperson in a year.
Discrete
b. The time between customer arrivals to a bank ATM.
Continuous
c. The number of customers in Big Nick’s barber shop.
Discrete
d. The amount of fuel in your car’s gas tank.
Continuous
e. The number of minorities on a jury.
Discrete
f. The outside temperature today.
Continuous
Chapter 6 Exercise 14
The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of
the time of mailing. Six letters are randomly sent to different locations.
a. What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.)
Probability 0.7351
b. What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal
places.)
Probability 0.2321
c. Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal
place.)
Number of letters 5.7
d-1. Compute the variance of the number that will arrive within 2 days. (Round your answer to 3
decimal places.)
Variance 0.285
d-2. Compute the standard deviation of the number that will arrive within 2 days. (Round your answer
to 4 decimal places.)
Standard Deviation 0.5339
Chapter 6 Exercise 20
In a binomial distribution, n = 12 and π = .60.
a. Find the probability for x = 5? (Round your answer to 3 decimal places.)
Probability 0.101
b. Find the probability for x ≤ 5? (Round your answer to 3 decimal places.)
Probability 0.157
c. Find the probability for x ≥ 6? (Round your answer to 3 decimal places.)
Probability 0.843
Chapter 6 Exercise 26
A population consists of 15 items, 10 of which are acceptable.
a. In a sample of four items, what is the probability that exactly three are acceptable? Assume the
samples are drawn without replacement. (Round your answer to 4 decimal places.)
Probability 0.4396
Chapter 7 Exercise 4
According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per
year on all types of insurance. Suppose the money spent is uniformly distributed between these
amounts.
a. What is the mean amount spent on insurance?
Mean $2,100
b. What is the standard deviation of the amount spent? (Round your answer to 2 decimal places.)
Standard deviation $981.49
c. If we select a family at random, what is the probability they spend less than $2,000 per year on
insurance per year? (Round your answer to 4 decimal places.)
Probability 0.4706
d. What is the probability a family spends more than $3,000 per year? (Round your answer to 4 decimal
places.)
Probability 0.2353
Chapter 7 Exercise 10
The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to
2 decimal places.)
a. About what percent of the observations lie between 55 and 65?
Percentage of observations 68.26%
b. About what percent of the observations lie between 50 and 70?
Percentage of observations 95.44%
c. About what percent of the observations lie between 45 and 75?
Percentage of observations 99.74%
Chapter 7 Exercise 14
A normal population has a mean of 12.2 and a standard deviation of 2.5.
a. Compute the z value associated with 14.3. (Round your answer to 2 decimal places.)
Z 0.84
b. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal
places.)
Proportion 0.2990
c. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)
Proportion 0.1894
Chapter 7 Exercise 18
A normal population has a mean of 80.0 and a standard deviation of 14.0.
a. Compute the probability of a value between 75.0 and 90.0. (Round intermediate calculations to 2
decimal places. Round final answer to 4 decimal places.)
Probability 0.4017
b. Compute the probability of a value of 75.0 or less. (Round intermediate calculations to 2 decimal
places. Round final answer to 4 decimal places.)
Probability 0.3594
c. Compute the probability of a value between 55.0 and 70.0. (Round intermediate calculations to 2
decimal places. Round final answer to 4 decimal places.)
Probability 0.2022
Chapter 7 Exercise 28
For the most recent year available, the mean annual cost to attend a private university in the United
States was $26,889. Assume the distribution of annual costs follows the normal probability distribution
and the standard deviation is $4,500.
a. Ninety-five percent of all students at private universities pay less than what amount? (Round z value
to 2 decimal places and your final answer to the nearest whole number.)
Amount $34,314