Question

If 80% of the applicants are able to pass a driver’s proficiency road test, find the mean, variance, and standard deviation of the number of people who pass the test in a sample of 300 applicants.

Answer 1

Let us consider X be the random variable denotes that the number of drivers (s) able to pass driver’s proficiency test in the sample of 100 applicants

 

Clearly, X ~ bin(300, 0.8)

n = 300, p = 0.8

 

Now, we want to find mean, variance and standard deviation of the number of people who pass the test in a sample of 300 applicants

 

E(X) = n ∙ p

        = 300 × 0.8

       = 240

 

V(X) = n ∙ p(1 – p)

       = 300(0.8)(1 – 0.8)

       = 48

 

S.D(X) = √V(X)

           = √48

           ≈ 6.928

E(X) = 240

 

V(X)= 48

 

S.D(X) ≈ 6.928