Fast Food and Gas Stations 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.
a. What are the mean and variance of x?
b. Calculate the interval µ±2σ . What values of the binomial random variable x fall into this interval?
c. Find P(6 ≤ x ≤ 14). How does this compare with the fraction in the interval µ±2σ for any distribution? For mound-shaped distributions?
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