Question

The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.025 failures per hour. (a) What is the probability that the instrument does not fail in an 8-hour shift

Answer 1

Answer: 0.1353

Explanation:

Given : The mean of failures = 0.025 per hour.

Then for 8 hours , the mean of failures =
`\lambda=8*0.25=2` per eight hours.

Let X be the number of failures.

The formula to calculate the Poisson distribution is given by :_

`P(X=x)=(e^(-\lambda)\lambda^x)/(x!)`

Now, the probability that the instrument does not fail in an 8-hour shift :-

`P(X=0)=(e^(-2)2^0)/(0!)=0.1353352\approx0.1353`

Hence, the the probability that the instrument does not fail in an 8-hour shift = 0.1353