1 what is the probability a vacationer will visit at least

Question

Problem 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.

1. What is the probability a vacationer will visit at least one of these attractions?

2. What is the probability .35 called?

3. Are the events mutually exclusive?

Problem 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).

Problem 3: Solve the following:

a. 20I/17I

_{b. 9}P ₃

_{c. 7}C ₂

Problem 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.

Problem 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.

1. What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.)
2. What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.)
3. Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal place.)
4. Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.)
5. Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)

Problem 6: In a binomial distribution, n = 12 and π = .60

1. Find the probability for x = 5? (Round your answer to 3 decimal places.)
2. Find the probability for x ≤ 5? (Round your answer to 3 decimal places.)
3. Find the probability for x ≥ 6? (Round your answer to 3 decimal places.)

Problem 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.

Problem 8: The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places.)

1. About what percent of the observations lie between 55 and 65?
2. About what percent of the observations lie between 50 and 70?
3. About what percent of the observations lie between 45 and 75?

Problem 9: A normal population has a mean of 12.2 and a standard deviation of 2.5.

1. Compute the z value associated with 14.3. (Round your answer to 2 decimal places.)
2. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.)
3. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)

Problem 10: A normal population has a mean of 80.0 and a standard deviation of 14.0.

1. Compute the probability of a value between 75.0 and 90.0.
2. Compute the probability of a value of 75.0 or less.
3. Compute the probability of a value between 55.0 and 70.0.

Problem 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?