A-machine-manufactures-washers-and-20-of-the-production-is-substandard-A-random-sample-o-f-10-washers-is-selected-Find-the-mean-and-standard-deviation-of-the-number-of-substandard-washers-in-the-s

Question Number 105670 by Ar Brandon last updated on 30/Jul/20

A machine manufactures washers, and 20 % of the production is

substandard . A random sample o f 10 washers is selected .

Find the mean and standard deviation of the number

of substandard washers in the sample .

Answered by Ar Brandon last updated on 30/Jul/20

This is a binomial probability distribution . Therefore;

mean, E (X) = np . Where n is the number of trials and

p is the probability of X on a trial . In this case n = 10, p = 20 %

\Rightarrow E (X) = 10 \times 0.2 = 2

For a binomial probability distribution,

variance, var (X) = np (1 - p) = 2 (1 - 0.2) = 1.6

standard deviation, σ = \sqrt{var (X)} = \sqrt{1.6} = 1.26 (to 3 S \cdot F)