Question

A batch of 15 electric motors actually contains four 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

X    HG (N = 15 , M = 4 , n = 3 , x = 4 )

Mean = nm / N
Mean = 3 * 4 / 15
Mean = 0.8

Variance

σ² = m ( N - m ) n ( N - n ) / N² ( N - 1 )
σ² = 4 ( 15 - 4 ) 3 ( 15 - 3 ) / 152 ( 15 - 1 )
σ² = 0.5029