Question

A study found that 1% of Social Security recipients are too young to vote. If 800 social security recipients are randomly selected find the Mean, Variance and the Standard deviation of social security recipients who are too young to vote. Present your answer in two decimal places and in order: mean, Variance, Standard deviation.

Answer 1

8, 7.92, 2.81

Explanation:

For each Social Security recipient, there are only two possible outcomes. Either they are too young to vote, or they are not. The probability of a Social Security recipient is independent of any other Social Security recipient. So we use 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 variance of the binomial distribution is:

`V(X) = np(1-p)`

The standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p))`

In this problem, we have that:

`n = 800, p = 0.01`

So

Mean:

`E(X) = np = 800*0.01 = 8`

The variance of the binomial distribution is:

`V(X) = np(1-p) = 800*0.01*0.99 = 7.92`

The standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p)) = √(800*0.01*0.99) = 2.81`

Formatted answer: 8, 7.92, 2.81