Assume that the weights of individuals are independent and normally distributed with a mean of 76Kg and a standard deviation of 16 Kg. Suppose that 25 people squeeze into an elevator that is designed to hold 1950 Kg.

(a) What is the average and standard deviation of the total weight inside the elevator?

(b) What is the probability that the load (total weight) exceeds the design limit?

(c) Assume that electricity costs 0.1 QAR per Kg for the first 10 persons and it is 0.2

QAR per Kg for any extra person getting into the elevator after the first 10 persons. Find the mean of the total electricity cost and its variance for the total number of people who squeezed inside the elevator.