Question

The proportion of adult women in a certain geographical region is approximately 49%. A marketing survey telephones 200 people at random.

​a) What proportion of the sample of 200 would you expect to be​ women?

​b) What would the standard deviation of the sampling distribution​ be?

​c) How many​ women, on​ average, would you expect to find in a sample of that​ size?

Answer 1

Let denotes the sample proportion of adult women out of 200 sampled person.

Since sample size is quite large enough ( > 30) , so can use Central Limit Theorem and approximate the distribution by normal distribution and we can write,

or

a) The expected proportion in a random sample of 200 people =

b) The standard deviation of the sampling distribution​ is =

c) Expected number of women in a random sample of 200 people = 200*0.49 = 98