Question

Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are well approximated by the normal distribution with mean 46.3 minutes and standard deviation 13.6 minutes. A random sample of 7 deliveries is selected. a) What is the probability that a particular delivery will arrive in less than one hour? Round your answer to four decimal places. b) What is the probability that the mean time of 7 deliveries will exceed one hour? Round your answer to four decimal places. c) Between what two times do the middle 60% of the average delivery times fall? and Round your answers to two decimal places. d) What is the probability that, in a random sample of 7 deliveries, more than three will arrive in less than an hour? Round your answer to four decimal places.

Answer 1

a)

Let X denote the delivery time (in minutes). Then

Required probability =

b)

Using Central Limit theorem, we know,

Required probability =

c)

We want to find 'a' such that

Using probability tables,

d)

Let Y denote the number of deliveries that arrive in less than an hour. Then,

Required probability =