Question

Problem 5) Over a typical quarter of the year about one-third of the total Internet population buy goods on line to be shipped to them. Of those millions of people, approximately 67% select Economy Ground shipping, which takes 5-7 days. A survey of 1000 randomly selected online shoppers is to be taken to see if they select Economy Ground or not. We are interested in the proportion of shoppers who respond “yes” that they use Economy Ground: this is p̂.

a) Show that the normal approximation for p̂ is valid by verifying the three conditions. Show the arithmetic.

b) What is the approximate distribution of p̂: give the shape, mean, and standard deviation. When you calculate the standard deviation, round to 2 nonzero decimals. For example, if you calculate ??̂ to be 0.01234, round to 0.012. (To round, remember: if it’s 4 or below, let it go. If it’s 5 or above, give it a shove.)

c) What is the probability that the proportion of shoppers in the sample who select Economy Ground shipping for their order is larger than 70%? Use the probability in the normal table exactly as given for full credit.

Answer 1