A stockbroker has recorded the number of transactions executed in the last month for client

accounts. The monthly number of transactions is known to be normally distributed with mean 12

and standard deviation 2.8.

Required:

(a) Calculate the probability that the number of transactions in the last month for a randomly

selected client account is less than 10.

(b) The firm selected a random sample of 16 client accounts. The mean number of

Transactions was 10.1.Use a hypothesis test to examine whether the mean of the sample is

Significantly different from that of the population at a significance level of 99%.

(c) The firm charges all clients a brokerage fee of 9.50 per transaction. The firm has

12,500 clients. Calculate the expected annual revenue from transaction fees.