In a sample of 800 U.S. adults, 172 dine out at a restaurant more than once per

ID: 3320285 • Letter: I

Question

In a sample of 800 U.S. adults, 172 dine out at a restaurant more than once per week. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through (d):

(a) Find the probability that both adults dine out more than once per week. The probability that both adults dine out more than once per week is [ ]. (Round to three decimal places as needed.)

(b) Find the probability that neither adult dines out more than once per week. The probability that neither adult dines out more than once per week is [ ]. (Round to three decimal places as needed.)

(c) Find the probability that at least one of the two adults dines out more than once per week is [ ] (Round to three decimal places as needed.)

(d) Which of the events can be considered unusual? Explain. Select all that apply:

A. The event in part (c) is unusual because its probability is less than or equal to 0.05.

B. None of these events are unusual.

C. The event in part (a) is unusual because its probability is less than or equal to 0.05.

D. The event in part (b) is unusual because its probability is less than or equal to 0.05.

Explanation / Answer

Since the sample is representative of all US adults, the probability that an adult selected at from all of US adults dines out at a restaurant more than once per week = 172/800 = 0.215. Two adults are selected at random without replacement.

a) P(both the adult dine out more than once per week) = 0.215*0.215=0.046

b) P(neither adult dines out more than once per week) = (1-0.215)(1-0.215) = 0.616

c) P(atleast one of two adults dines out more than once per week) = 1 - P(neither adult dines more than once per week) = 1 - 0.616 = 0.384

d) Clearly, with such a low probability of an adult dining more than once per week, it is unusual for an event in part(a) to occur i.e for both the adults to dine more than once per week. Also its probability is less than 0.05

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In a sample of 800 U.S. adults, 171 dine out at a resaurant more than once per w

In a sample of 800 U.S. adults, 202 dine out at a resaurant more than once per w

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In a sample of 800 U.S. adults, 172 dine out at a restaurant more than once per

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