1. Lead timeis 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,, for a particular supplier of men's apparel, the purchasing department of a national department store chain randomly sampled 64 of the supplier's lead times and foundx=44 days. [30 points]
2. Describe the shape of the sampling distribution ofx. Justify your answer. [10 points]

3. If and are really 38 and 12, respectively, what is the probability that a second random sample of size 64 would yieldxgreater than or equal to 41? [10 points]

4.

Using the values for and in partb,what is the probability that a sample of size 64 would yield a sample mean within the interval2n ? [10 points]