A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is
A)0.4332
B)0.9332
C)0.0668
D)0.5668

Question

Quizplus · Accepted Answer

We will use the central limit theorem since the sample size is large enough.
The mean of the sampling distribution of proportions is equal to the population proportion, which is 0.8.
The standard deviation of the sampling distribution of proportions is calculated as follows: 
sqrt( (p*(1-p))/n ) = sqrt( (0.8*0.2)/400 ) = 0.026
Now, we need to standardize the value of 0.83:
z = (0.83 - 0.8) / 0.026 = 1.15
Using a standard normal distribution table, we find that the probability of z being greater than 1.15 is 0.0668. Therefore, the answer is C.

A Sample of 400 Observations Will Be Taken from an Infinite