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

Answer:

$P(X = 2) = 0.2613$

Step-by-step 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:

$P(X = x) = \frac{e^{-u} u^x}{x!}$

Where

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

$u = np$

$u = 60 * 4\%$

$u = 60 * 0.04$

$u = 2.4$

So:

$P(X = x) = \frac{e^{-u} u^x}{x!}$ becomes

$P(X = 2) = \frac{e^{-2.4}2.4^{2}}{2!}$

$P(X = 2) = \frac{e^{-2.4}* 5.76}{2}$

$P(X = 2) = e^{-2.4}* 2.88$

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

$P(X = 2) = 0.26126770544$

$P(X = 2) = 0.2613$

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