Solve the following:
Q1: 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?
b. Which concept of probability did you use to make this estimate?
Q2: 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.)
b. Use the complement rule to find the probability it will not lose money next quarter. (Round your answer to 2 decimal places.)
Q3: 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.)
b. What is the probability .35 called?
c. Are the events mutually exclusive?
Q4: 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).
P(A3|B1)
Q5: Solve the following:
a.9P3
b. 7C2
Q6: 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?
b. What is the probability that exactly five arrive within 2 days?
c. Find the mean number of letters that will arrive within 2 days.
Number of letters
d-1. Compute the variance of the number that will arrive within 2 days.
d-2. Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)
Q7: 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?
b. What is the probability that exactly five arrive within 2 days?
c. Find the mean number of letters that will arrive within 2 days.
d-1. Compute the variance of the number that will arrive within 2 days.
d-2. Compute the standard deviation of the number that will arrive within 2 days.
Q8: In a binomial distribution, n = 12 and π = .60.
a. Find the probability for x = 5?
b. Find the probability for x ≤ 5?
c. Find the probability for x ≥ 6?
Q9: A population consists of 15 items, 10 of which are acceptable.
In a sample of four items, what is the probability that exactly three are acceptable? Assume the samples are drawn without replacement.
Q10: 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?
b. What is the standard deviation of the amount spent?
c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year?
d. What is the probability a family spends more than $3,000 per year?
Q11: The mean of a normal probability distribution is 60; the standard deviation is 5.
a. About what percent of the observations lie between 55 and 65?
b. About what percent of the observations lie between 50 and 70?
c. About what percent of the observations lie between 45 and 75?
Q12: 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.
b. What proportion of the population is between 12.2 and 14.3?
c. What proportion of the population is less than 10.0?
Q13: 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.
b. Compute the probability of a value of 75.0 or less.
c. Compute the probability of a value between 55.0 and 70.0.
Q14: 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.
Ninety-five percent of all students at private universities pay less than what amount?