Question

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 customer will arrive in 10 minutes interval

ii.) Exactly 2 customers will arrive in 10 minutes interval

iii.) At most 2 customers will arrive in 10 minutes interval

iv.) At least 3 customers will arrive in 10 minutes interval

(c) In a mainframe computer center, 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

Answer 1