Market research of supermarket sales indicates that impulse buying in a supermarket is time-dependent. Keeping costumers in the store longer via tasting events, long check out lines, etc., results in higher expenditures on items not on shopping lists.

Let x represent the dollar amount spent on impulse buying in an unplanned 10 minute shopping interval. Based on an article in the Denver Post, the population is approximately normal with a mean of $19.75 and a standard deviation of $7.05.

a. What is the probability that an individual shopper spends between $17.25 and $21.60 on impulse buys?

b. What is the probability that a random sample of 50 shoppers will have a mean between $17.25 and $21.60?

c. describe why the answers from part (a) and (b) are different.

d. What would happen to the probability in part b if the sample size was increased to n = 100? describe why this happens.