Question

New York State has found that 30 % of all consumer complaints are valid. If the State received 6000 complaints last year, about how many of them are expected to be valid ? Find the standard deviation.

Answer 1

Answer:

1800 of the complaints are expected to be valid.

The standard deviation is 35.5 complaints.

Step-by-step explanation:

For each consumer complaint, there are only two possible outcomes. Either it is valid, or it is not. So we use concepts of the binomial probability distribution to solve this question.

Binomial probability distribution

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

The expected value 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, we have that:

$n = 6000, p = 0.3$

How many of them are expected to be valid?

$E(X) = np = 6000*0.3 = 1800$

1800 of the complaints are expected to be valid.

Find the standard deviation.

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6000*0.3*0.7} = 35.5$

The standard deviation is 35.5 complaints.