Question

Suppose a simple random sample of size n=75 is obtained from a population whose size is N= 25,000

and whose population proportion with a specified characteristic is p=0.2.

​(c) What is the probability of obtaining x=99 or fewer individuals with the​ characteristic? That​ is, what is

​P(p ≤ 0.12)?

​(Round to four decimal places as​ needed.)

Answer 1

Solution:

Given ,

p = 0.2 (population proportion)

n = 75 (sample size)

Let x be the number of successes in the sample.

Let be the sample proportion.

= x/n

The sampling distribution of   is approximately normal with

mean = =  p = 0.

SD =   =   

=

= 0.04618802153

Now ,

​P(  ≤ 0.12)

=

=  P(Z <(0.12 -0.2)/0.04618802153)

= P(Z < -1.73)

= 0.0418 ...use z table

Required probability = 0.0418