(a) During any eight-hour shift. the proportion of time, X and the density function of a

sheet- metal stamping machine being down for maintenance or repairs is given as

follows:

f(x)- {2(1-x), 03x31

0, elsewhere

The cost (in hundreds of P) of this downtime. due to lost production and cost of

maintenance and repair. is given by C = 10 + 20X + 4X2 . Find the mean and variance of

C.

(b) During peak hours, the arrival of customers at a fast food restaurant is random with an

average rate of 90 customers per hour-

(i) Calculate the probability that exactly two customers will arrive at the restaurant

within a specified one-minute during peak hours.

(ii) Calculate the probability that at least for

Q1 (a) During any eight-hour shift, the proportion of time, X and the density function of a sheet- metal stamping machine being down for maintenance or repairs is given as follows: f(x) = 2(1-x), osx51 0, elsewhere The cost (in hundreds of P) of this downtime, due to lost production and cost of maintenance and repair, is given by C = 10 + 20X + 4X2 . Find the mean and variance of C. (6 marks) (b) During peak hours, the arrival of customers at a fast food restaurant is random with an average rate of 90 customers per hour. (i) Calculate the probability that exactly two customers will arrive at the restaurant within a specified one-minute during peak hours. (4 marks) (ii) Calculate the probability that at least for customers will arrive within a specified two-minute period during peak hours. (4 marks)