Question

A random sample of size n = 50 is selected from a binomial distribution with population proportion

p = 0.8.

Describe the approximate shape of the sampling distribution of p̂.

Calculate the mean and standard deviation (or standard error) of the sampling distribution of p̂. (Round your standard deviation to four decimal places.)

mean =

standard deviation =

Find the probability that the sample proportion p̂ is less than 0.9. (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

p = 0.8

1 - p = 0.2

n = 50

The approximate shape of the sampling distribution of p̂.

N ( , )

Mean:

= p = 0.8  

standard deviation:

= (p*(1-p))/n =  (0.8*0.2)/50 = 0.0566

P( < 0.9) = P(( - ) / < (0.9 - 0.8) / 0.0566)

= P(z < 1.77)

= 0.9616

Probability = 0.9616