Question

Suppose that in the population, exactly 40% of all students who apply to medical school are accepted. If many random samples of size n = 475 students are selected from this population, we know the sample proportion who are accepted to medical school will vary from sample to sample. The sampling distribution of the sample proportion would be Normal in shape and would have a standard deviation equal to what value?

A. 0.0010

B. 0.0225

C. 0.0459

D. 0.4000

E. 0.4750

Answer 1

Solution:

Given ,

p = 40% = 0.40 (population proportion)

n = 475 (sample size)

Let be the sample proportion.

The sampling distribution of is approximately normal with

mean = =  p = 0.40

SD =   =     

=  \sqrt{0.40(1-0.40)/475}

= 0.0225

Answer: 0.0225