Question

A history class has 75 members. If there is a 12% absentee rate per class meeting, find the mean, variance, and standard deviation of the number of students who will be absent from each class.

Answer 1

Let us consider X be the random variable denotes that the number of absents in the history class of 75 members.

Clearly, x~ bin(75, 0.12)

n = 75

p = 0.12

 

Now, we want to find mean, variance and standard deviation of the number of students who will be absent from each class

Mean,

E(X) = n ∙ p

       = 75 × 0.12

       = 9

 

Variance,

V(X) = np(1 – p)

       = 75 × (0.12)(1 – 0.12)

       = 7.92

 

Standard deviation,

S.D(X) = √V(x)

           = √7.92

           ≈ 2.8142

Mean = 9

 

Variance = 7.92

 

Standard deviation ≈ 2.8142