QUESTION 1 (12 MARKS)

In order to encourage car-pooling doings, a new toll charge is to be introduced on the ERIZ Expressway. A charge of RM3, RM2, RM1, and RM0 are to be charged to 0, 1, 2, and 3 or more passengers respectively.

TABLE 1 shows a probability distribution for the number of passengers in a single car.

TABLE 1

x 0 1 2 3

P(X = x) 0.40 0.35 0.20 0.05

a) Construct a probability distribution for the toll charged. (Hint: Let Y be the toll charged). (3 marks)

b) Find the probability that at most RM2 is being charged for the toll. (2 marks)

c) According to ERIZ Expressway's officer, an RM1.50 toll charge is expected to be paid per car. Is the officer expectation true? Justify your answer. (3 marks)

d) Calculate the standard deviation of tolls charged. (4 marks)