If the population proportion is 0.90 and a sample of size 64 is taken,what is the probability that the sample proportion is less than 0.88?
A) 0.2019
B) 0.2981
C) 0.5300
D) 0.7019
E) 0.7899

Question

Quizplus · Accepted Answer

The sample proportion, p-hat, follows a normal distribution with a mean of the population proportion, which is 0.90, and a standard deviation of the square root of [(0.90)(0.10)/64] = 0.0375. 
To find the probability of the sample proportion being less than 0.88, we can standardize the sample proportion to a standard normal distribution: 
(z-score) = (0.88 - 0.90)/0.0375 = -0.5333 
Using a standard normal distribution table or calculator, we find that P(z < -0.5333) = 0.2981.

If the Population Proportion Is 0