1.The time to deliver packaged containers by a logistics company is found from

samples of size 4. The mean and standard deviation of delivery times is estimated to

be 140 hours and 6 hours, respectively.

(a) Find the 2 sigma and 3 sigma control limits for the average delivery time.

(b) Explain a type I and type II error specifically in this context.

(c) If the mean delivery time shifts to 145 hours, what is the probability of not

detecting this by the second sample after the shift?

(d) What is the ARL? Explain.