Question

A company manufactures batteries in batches of 26 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch.

Answer 1

Answer:

The standard deviation for the number of defects per batch is 0.87.

Step-by-step explanation:

Let X denote the number of defective batteries per batch.

A company manufactures batteries in batches of n = 26.

It is provided that the rate of defects is, p = 0.03.

Each battery is defective independently of the others.

The random variable X follows a binomial distribution.

The standard deviation of a binomial distribution is:

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

Compute the standard deviation for the number of defects per batch as follows:

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

  $=\sqrt{26\times 0.03\times (1-0.03)}\\\\=0.86982757\\\\\approx 0.87$

Thus, the standard deviation for the number of defects per batch is 0.87.