Each customer in a shop, independently of other customers, spends an amount which is given by a random variable with mean R240 and standard deviation R80. Let S be the amount spent by the first 100 customers to visit the shop.

(a) Give the mean and standard deviation of S.

(b) Use Chebyshev's inequality to give a lower bound for P(23 000 S 25 000).

(c) Assume that the amount spent by each customer follows the normal distribution. Compute the same probability P(23 000 S 25 000).