Question

Six percent of computer chips produced by Cheapo Chips are defective. Each month a random sample of 200 chips manufactured that month are taken. Let X = the number of defective chips in the sample. What are the mean and standard deviation of X?

Answer 1

Using the binomial distribution, it is found that the mean of X is of 12, with a standard deviation of 3.36.

For each chip, there are only two possible outcomes, either it is defective, or it is not. The probability of a chip being defective is independent of any other chip, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.  

The mean of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem:

• Six percent of computer chips produced by Cheapo Chips are defective, hence $p = 0.06$.

• Each month a random sample of 200 chips manufactured that month are taken, hence $n = 200$

Then:

$E(X) = np = 200(0.06) = 12$

$\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{200(0.06)(0.94)} = 3.36$

The mean of X is of 12, with a standard deviation of 3.36.

A similar problem is given at brainly.com/question/12473640