Question: Tony Hsieh is CEO of e-tailer Zappos.com. His company sells shoes online. It differentiates itself by its selection of shoes and a devotion to customer service. It offers free shipping and free return shipping. An area in which costs could be cut back is the shipping charges for return shipping, specifically those that result from the wrong size of shoes being sent. Zappos may try to keep the percentage 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 Zappos has kept the percentage of returns due to incorrect size to no more than 5%. Support your answer with statistical reasoning.

d. If Zappos 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.