QUESTION ONE:
(a) Based on past experience, the quality control engineer of Heavy Electrical Limited has estimated that the probability of commissioning each project in time at a site is 0.9. The company is planning to commission 5 such projects in the forthcoming year. Find the probability of commissioning:
i.) No project
ii.) Two projects in time
iii.) At most one project in time
iv.) At least two projects in time
v.) Find the mean and variance of the above distribution
(b) The arrival rate of customers arriving at a bank counter follows a Poisson distribution with a mean rate of 4 per 10 minutes interval. Find the probability that:
i.) Exactly 0 customers will arrive in a 10-minute interval
ii.) Exactly 2 customers will arrive in a 10-minute interval
iii.) At most 2 customers will arrive in a 10-minute interval
iv.) At least 3 customers will arrive in a 10-minute interval
(c) In a mainframe computer center, the execution time of programs follows an exponential distribution. The average execution time of the programs is 5 minutes. Find the probability that the execution time of programs is:
i.) Less than 4 minutes
ii.) More than 6 minutes