Fast Computers Inc. supplies made-to-order personal computers through direct (telephone and online) sales channels. A key competitive feature of its business is the delivery time - the time lapse between receipt of an order and final delivery to the customer.By tracking thousands of previous orders, the company has found that delivery times to the large Toronto market are well-approximated by a normal distribution with a mean value of 4.5 days and standard deviation of 3.14 days.In answering the following questions, you may assume that these parameters are known exactly.

a)What is the probability that a randomly selected order will require more than six days?

b)What is the probability that a randomly selected order will require between three and six days?

c)The company is considering a $50 cash-back guarantee on any orders that have delivery times longer than a specified maximum but are not sure what maximum time to guarantee.They would be willing to pay out the guarantee on no more than 3% of their deliveries.What time limit in whole days should they set for their guarantee?

d)What is the probability that the mean time for a sample of fifteen randomly selected orders will be more than six days?