An online shoe retailer has the goal of keeping the percent of returns due to incorrect size to no more than 5%. The file titled Shoesize contains a sample of 125 shoe sizes that were sent to customers and the sizes that were actually ordered.

a. Determine the number of pairs of wrong-size shoes that were delivered to customers.

b. Calculate the probability of obtaining at least that many pairs of wrong-sized shoes delivered to customers if the proportion of incorrect sizes is actually 0.05.

c. On the basis of your calculation, determine whether the retailer has kept the percent of returns due to incorrect size to no more than 5%. Support your answer with statistical reasoning.

d. If the company sells 5 million pairs of shoes in one year and it costs an average of $4.75 a pair to return them, calculate the expected cost associated with wrong-sized shoes being returned using the probability calculated from the sample data.