Surveys show that 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 that in a store. Suppose a random sample of 2500 U. S. adults were asked if they agree or disagreed with the statement, "I prefer to shop for clothes online rather than in store." Let pp^ be the proportion of people in the sample that prefer to (a) What is the shape, mean, and standard deviation of the sampling distribution of pp^?

(b) Of the pool 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 manager's claim is true.

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