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Introduction to Probability and Statistics 1 | 14th Edition | ISBN: 9781133103752 | Authors: William Mendenhall Robert J. Beaver, Barbara M. Beaver
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Fast Food and Gas Stations Forty percent ofall Americans who travel by car look for gas

Chapter 5, Problem 32

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QUESTION:

Fast Food and Gas Stations Forty percent ofall Americans who travel by car look for gas stationsand food outlets that are close to or visible from thehighway. Suppose a random sample of n 25 Americanswho travel by car are asked how they determinewhere to stop for food and gas. Let x be the number inthe sample who respond that they look for gas stationsand food outlets that are close to or visible from thehighway.a. What are the mean and variance of x?b. Calculate the interval m 2s. What values of thebinomial random variable x fall into this interval?c. Find P(6 x 14). How does this compare withthe fraction in the interval m 2s for any distribution?For mound-shaped distributions?

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QUESTION:

Fast Food and Gas Stations Forty percent ofall Americans who travel by car look for gas stationsand food outlets that are close to or visible from thehighway. Suppose a random sample of n 25 Americanswho travel by car are asked how they determinewhere to stop for food and gas. Let x be the number inthe sample who respond that they look for gas stationsand food outlets that are close to or visible from thehighway.a. What are the mean and variance of x?b. Calculate the interval m 2s. What values of thebinomial random variable x fall into this interval?c. Find P(6 x 14). How does this compare withthe fraction in the interval m 2s for any distribution?For mound-shaped distributions?

ANSWER:

Step 1 of 4

Given that,

Forty percent of all Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway. Suppose a random sample of n = 25 Americans who travel by car are asked how they determine where to stop for food and gas. Let x be the number in the sample who respond that they look for gas stations and food outlets that are close to or visible from the highway.

The given information indicates that x follows binomial distribution with parameters n = 25 and p = 0.40.

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