Reference no: EM13907254

1. 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?

b. What is the probability .35 called?

c. Are the events mutually exclusive?

2. 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).

3. 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.

4. 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?

5. 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.

6. 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?

7. 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?

8. 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.

9. 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?