New Horizons Inc. markets durable ‘travel clothing' through direct (telephone and online) sales channels. A key competitive feature of their business is the delivery time - the time lapse between receipt of an order and final delivery to the customer. The company has found that delivery times to their large Toronto market approximately follow a normal distribution with a mean value of 4.3 days and standard deviation of 1.2 days.
a) What is the probability that a randomly selected order will require more than five days?
b) What is the probability that a randomly selected order will require between three and five days?
c) The company is considering a cash-back guarantee on any orders that have delivery times above a specified maximum. They would be willing to pay out this guarantee on no more than 5% 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 nine randomly selected orders will be more than five days?