Consider a binomial experiment with

n = 10

and

p = 0.40.

(a)

Compute

f(0).

(Round your answer to four decimal places.)

f(0) =

(b)

Compute

f(2).

(Round your answer to four decimal places.)

f(2) =

(c)

Compute

P(x = 2).

(Round your answer to four decimal places.)

P(x = 2) =

(d)

Compute

P(x = 1).

(Round your answer to four decimal places.)

P(x = 1) =

(e)

Compute

E(x).

E(x) =

(f)

Compute

Var(x)

and s. (Round your answer for s to two decimal places.)

Var(x)

=

s =

You may need to use the appropriate appendix table or technology to answer this question.

A center for medical services reported that there were 295,000 appeals for hospitalization and other services. For this group, 45% of first-round appeals were successful. Suppose 10 first-round appeals have just been received by a Medicare appeals office. (Round your answers to four decimal places.)

(a)

Compute the probability that none of the appeals will be successful.

(b)

Compute the probability that exactly one of the appeals will be successful.

(c)

What is the probability that at least two of the appeals will be successful?

(d)

What is the probability that more than half of the appeals will be successful?

You may need to use the appropriate appendix table or technology to answer this question.

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (Round your answers to four decimal places.)

(a)

Compute the probability that 2 or fewer will withdraw.

(b)

Compute the probability that exactly 4 will withdraw.

(c)

Compute the probability that more than 3 will withdraw.

(d)

Compute the expected number of withdrawals.

Consider a Poisson distribution with a mean of three occurrences per time period.

(a)

Write the appropriate Poisson probability function.

f(x) =

(b)

What is the expected number of occurrences in four time periods?

(c)

Write the appropriate Poisson probability function to determine the probability of x occurrences in four time periods.

f(x) =

(d)

Compute the probability of three occurrences in one time period. (Round your answer to four decimal places.)

(e)

Compute the probability of twelve occurrences in four time periods. (Round your answer to four decimal places.)

(f)

Compute the probability of eleven occurrences in three time periods. (Round your answer to four decimal places.)

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You may need to use the appropriate appendix table or technology to answer this question.

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.)

(a)

Compute the probability of receiving three calls in a 5-minute interval of time.

(b)

Compute the probability of receiving exactly 10 calls in 15 minutes.

(c)

Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?

What is the probability that none will be waiting?

(d)

If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?

You may need to use the appropriate appendix table or technology to answer this question.

Emergency 911 calls to a small municipality in Idaho come in at the rate of one every two minutes.

(a)

What is the expected number of calls in one hour?

(b)

What is the probability of three calls in five minutes? (Round your answer to four decimal places.)

(c)

What is the probability of no calls in a five-minute period? (Round your answer to four decimal places.)

Suppose

N = 10

and

r = 3.

Compute the hypergeometric probabilities for the following values of n and x. (Round your answers to four decimal places.)

(a)

n = 4, x = 1

(b)

n = 2, x = 2

(c)

n = 2, x = 0

(d)

n = 4, x = 2

(e)

n = 4, x = 4

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Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 35 employees; the Hawaii plant has 25. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. (Round your answers to four decimal places.)

(a)

What is the probability that none of the employees in the sample work at the plant in Hawaii?

(b)

What is the probability that 1 of the employees in the sample works at the plant in Hawaii?

(c)

What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii?

(d)

What is the probability that 9 of the employees in the sample work at the plant in Texas?

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The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 restaurants located in a certain city, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to this city and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Busine

associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner. (Round your answers to four decimal places.)

(a)

What is the probability that none of the meals will exceed the cost covered by your company?

(b)

What is the probability that one of the meals will exceed the cost covered by your company?

(c)

What is the probability that two of the meals will exceed the cost covered by your company?

(d)

What is the probability that all three of the meals will exceed the cost covered by your company?