Question

In a factory , the machines break down and require service according to Poisson distribution at the average of 4 per day .

What is the probability that exactly 6 machines break down in 2 days ?

A) 0.12214

B) 0.10419

C) 0.42304

D) 0.03296

E) 0.90840

Answer 1

solution:

From the given information

Let X be the discrete random variable representing no.of machines break down in 2 days period

If the machines require service at the rate of 4 per day

Then, machines require service at the rate of 8 per 2 days

= 8

Here,, X~Po(8)

P(X=x) = e^(-) * ()^x / x!

Now, Probability that exactly 6 machines break down in 2 days = P(X=6)

=

= 0.122138

~ 0.12214

Probability that exactly 6 machines break down in 2 days = 0.12214

So,Option-A is correct