1. Surveys show that fewer people enjoy shopping in stores than in the past. A manager of a clothing store
claims that 60% of all U.S. adults prefer shopping for clothes online rather than in a store. Suppose a random sample of 2500 U.S. adults were asked if they agreed or disagreed with the statement, "I
prefer to shop for clothes online rather than in a store”. Let pp be the proportion of people in the sample that prefer to shop for clothes online rather than in a store.

(a) What is the shape, mean, and standard deviation of the sampling distribution?

(b) of the poll respondents, 63% agreed. Find the probability of obtaining a sample of 2500 U.S. adults in which 63% or greater prefer shopping for clothes online, assuming the manger's claim is true.

(c) Based on your answer in part (b), do you have reason to doubt the manager's claim?