A restaurant offers pizza delivery service to a campus dormitory. Delivery times follow a normal ...

  

A restaurant offers pizza delivery service to a campus dormitory. Delivery times follow a normal distribution with mean 20 minutes and standard deviation 5 minutes. 

(a) The restaurant selected a random sample of 26 deliveries, what is the probability that the sample mean delivery time is between 18 and 23 minutes? 

(b) Suppose the restaurant plans to expand its delivery network, and offers service to commercial areas as well. A random sample of delivery times is required to estimate the new population mean of delivery time. How large a sample is needed to ensure the probability that the sample mean is larger than the new population mean by more than 2 minutes is less than 0.05? Assume the new population standard deviation is 10 minutes.