A National Park Service survey of visitors to the Rocky Mountain region

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

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). (Round your answer to 4 decimal places.)

P(A3|B1)

3.
Solve the following:
a.

b.
9P 3

c.
7C 2

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.

b. The time between customer arrivals to a bank ATM.

c. The number of customers in Big Nick’s barber shop.

d. The amount of fuel in your car’s gas tank.

e. The number of minorities on a jury.

f. The outside temperature today.

5.
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

b. What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.)

Probability

c. Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal place.)

Number of letters

d-1. Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.)

Variance

d-2. Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)

Standard Deviation

6.
In a binomial distribution, n = 12 and ? = .60.

a. Find the probability for x = 5? (Round your answer to 3 decimal places.)

Probability

b. Find the probability for x ? 5? (Round your answer to 3 decimal places.)

Probability

c. Find the probability for x ? 6? (Round your answer to 3 decimal places.)

Probability

7.
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. (Round your answer to 4 decimal places.)

Probability

8.
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 %

b. About what percent of the observations lie between 50 and 70?

Percentage of observations %

c. About what percent of the observations lie between 45 and 75?

Percentage of observations %

9.
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

b. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.)

Proportion

c. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)

Proportion

10.
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

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

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

11.
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? (Round z value to 2 decimal places and your final answer to the nearest whole number.)

Amount $