A warehouse distributor of carpet faces a normally distributed demand for its carpet. The average demand for carpet from the stores that purchase from the distributor is 4,500 yards per month, with a standard deviation of 900 yards.

a.Suppose the distributor keeps 6,000 yards of carpet in stock during a month. What is the probability that a customer's order will not be met during a month? (This situation is referred to as a stockout.)

b.What is the probability that the demand will be between 5000 and 7000 yards?

c.How many yards of carpet should this warehouse distributor order from its supplier to ensure that 97% of the demand is met? (The percent of customer demand/orders satisfied is referred to as service level. In this question, the service level is 97%.)