Question

11. Solve the problem. A company manufactures televisions in batches of 25 and there is a 1% rate of defects. Find the standard deviation for the number of defects per batch.

0.7

0.9

0.5

72.8

Answer 1

Answer: 0.5

Step-by-step explanation:

For binary distribution with parameters p (probability of getting success in each trial) and n (Total trials) , we have

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

We are given that ,

Total batches of televisions : n=25

The probability of defects : p= 0.01

Here success is getting defective batch .

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

$\sigma=\sqrt{(25)(0.01)(1-0.01)}\\\\=\sqrt{(25)(0.01)(0.99)}\\\\=\sqrt{0.2475}\\\\=0.497493718553\approx0.5$ [Rounedde to the nearest tenth.]

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