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 standard deviation of the number of recipients who are too young to vote.

Answer 1

Let us consider X be the random variable that denotes the number of social security recipients who are too young to vote among randomly selected 800 social security recipients.

 

From the study, n = 800, p = 0.01

Clearly, X~(bin(800,0.01)

•  
• Mean, E(X) = 800 × 0.01
•                     = 8

Variance, V(X) = 800 × 0.01 × (1 – 0.01)

                         = 7.92

 

Standard deviation,

S.D(X) = √V(X)

           = √7.92

           = 2.814249

            ≈ 2.814

• Mean, E(X) = 8

Variance, V(X) = 7.92

Standard deviation,

S.D(X) ≈ 2.814