Question

Specify the distribution, including the name and value(s) of parameter(s), of X in Exercise 1.

1. A batch of 15 electric motors actually contains three defective motors. An inspector chooses 3 (without replacement). Find the mean and variance of X, the number of defective motors in the sample.

Answer 1

Solution:

It is given that , 3 out of 15 are defective.

Let p be the probability of success of event "motor is defective"

p = 3/15 = 0.2

An inspector chooses 3 (without replacement).

So , n = 3 , where n denotes number of trials.

Let X be the number of defective motors in the sample.

X follows Binomial(n = 3 , p = 0.2)

For binomial distribution ,

Mean = n * p = 3 * 0.2 = 0.6

Mean of X is 0.6

Variance = n * p * (1 - p) = 3 * 0.2 * (1 - 0.2) = 0.48

Variance of X is 0.48