Question

if the mean no. of flawed items produced by a factory manufacture line per 2 hour period is two. Assume that the number of flawed items produced in a one-hour period is observed 9 times, thus giving 9 independent observations Y₁ , Y₂ ,...Y₉.. Find the probability that Y > 3 during at least one of the 9 one-hour intervals.

Answer 1

Given the mean number of flawed items produced by a factory manufacture line per 2 hour period is 2.

So we can say the average number of flawed items produced by a factory manufacture line per 1 hour period is 1.

We can say the number of flawed items produced by a factory manufacture line per 1 hour period is Poisson distributed with . Thew probability

The probability

The R command for the above probability is

> 1-ppois(3,1)
[1] 0.01898816

The probabilty that at least one of Y1, Y2,...,Y9 is greater than 3 is