Lead time is the time between a retailer placing an order and having the product available to satisfy customer demand. It includes time for placing the order, receiving the shipment from the supplier, inspecting the units received, and placing them in inventory. Interested in average lead time, m, for a particular supplier of men's apparel, the purchasing department of a national department store chain randomly sampled 50 of the supplier's lead times and found x̅ = 44 days.

a. Describe the shape of the sampling distribution of x.

b. If μ and σ are really 40 and 12, respectively, what is the probability that a second random sample of size 50 would yield x̅ greater than or equal to 44?

c. Using the values for m and s in part b, what is the probability that a sample of size 50 would yield a sample mean within the interval μ ± 2σ/√n?