Question

A company makes electric motors. The probability an electric motor is defective is 4%. What is the probability that a sample of 60 electric motors will contain exactly 2 defective motor?

Answer 1

`P(X = 2) = 0.2613`

Explanation:

Given

`p = 4\%` --- proportion

`x = 2` --- defective motors

`n = 60` --- sample size

Required

Determine the probability that exactly 2 is defective

This follows a Poisson distribution and will be solved using:

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

Where

u = Expected number of occurrence, and it is calculated as:

`u = np`

`u = 60 * 4\%`

`u = 60 * 0.04`

`u = 2.4`

So:

`P(X = x) = (e^(-u) u^x)/(x!)` becomes

`P(X = 2) = (e^(-2.4)2.4^(2))/(2!)`

`P(X = 2) = (e^(-2.4)* 5.76)/(2)`

`P(X = 2) = e^(-2.4)* 2.88`

`P(X = 2) = 0.09071795328* 2.88`

`P(X = 2) = 0.26126770544`

`P(X = 2) = 0.2613`

Hence, the probability that exactly 2 out of 60 will be defective is 0.2613