Question

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.

Answer 1

Answer:

There is a 25% chance that one will have defects in a batch

Step-by-step explanation:

Answer 2

Answer:

The standard deviation for the number of defects per batch is 0.495.

Step-by-step explanation:

For each batch television, there are only two outcomes. Either they are defective, or they are not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials of X, with p probability, and X can only have two outcomes.

Has a standard deviation of:

$\sqrt{Var(X)} = \sqrt{n*p*(1-p)}$

In this problem, we have that:

$n = 25, p = 0.01$

So

$\sqrt{Var(X)} = \sqrt{n*p*(1-p)} = \sqrt{25*0.01*0.99} = 0.495$

The standard deviation for the number of defects per batch is 0.495.