Question

A study found out that 1% of social security recipients are too young to vote. If 800 social security recipients are randomly selected, find the mean, variance and standard deviation of the number of recipients who are too young to vote

Answer 1

Mean :
`\mu=8`

Variance :
`\sigma^2=7.92`

Standard deviation =
`\sigma=2.81`

Explanation:

We know that , in Binary Distribution having parameters p (probability of getting success in each trial) and n (Total number trials) , the mean and variance is given by:-

Mean :
`\mu=np`

Variance :
`\sigma^2=np(1-p)`

We are given that ,

Total social security recipients : n=800

The probability of social security recipients are too young to vote : p=1%= 0.01

Here success is getting social security recipients are too young to vote .

Then, the mean, variance and standard deviation of the number of recipients who are too young to vote will be :-

Mean :
`\mu=800*0.01=8`

Variance :
`\sigma^2=800* 0.01(1-0.01)=8*0.99=7.92`

Standard deviation =
`\sigma=√(\sigma^2)=√(7.92)=2.81424945589\approx2.81`

Hence, the mean, variance and standard deviation of the number of recipients who are too young to vote :

Mean :
`\mu=8`

Variance :
`\sigma^2=7.92`

Standard deviation =
`\sigma=2.81`