Question

A company manufactures televisions in batches of 25 and there is a 1% rate of defects. Find

Answer 1

The standard deviation for the number of defects per batch is 0.5

Solution:

In binomial distribution, standard deviation is given as:

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

Where "n" is the number of observations

"p" is probability of getting success

We are given that ,

Total batches of televisions : n = 25

The probability of defects : p = 1% = 0.01

Here success is getting defective batch

Then, the standard deviation for the number of defects per batch will be:

Plugging in values in formula, we get

$\sigma=\sqrt{(25)(0.01)(1-0.01)}\\\\=\sqrt{(25)(0.01)(0.99)}\\\\=\sqrt{0.2475}\\\\=0.497493718553\approx0.5$

Therefore, the standard deviation for the number of defects per batch = 0.5