Question

A fair coin is flipped 100 times.

a. Describe the center, shape, and spread of the sampling distribution of the proportion of heads.

b. What conditions are satisfied that ensure your answers in part (a) are correct?

Answer 1

A)

Center (mean) = n*p

N = number of trials = 100

P = 0.5 (probability of single trial)

Mean = 100*0.5 = 50

Spread (standard deviation) = √n*p*(1-p) = 5

B)

Two conditions of normality must be satisfied

That is n*p and n*(1-p) should be greater than 5

N*p = 50 >5

N*(1-p) = 50 >5

Conditions are met, so by normal approximation

Shape is normal

Spread is 5

Center is 50