A sample of 400 observations will be taken from a process (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 can use the central limit theorem here since n = 400 > 30. The mean of the sample proportion is equal to the population proportion, which is 0.8. The standard deviation of the sample proportion is calculated as:
sqrt((0.8 * 0.2) / 400) = 0.02

To find the probability that the sample proportion will be greater than 0.83, we standardize the value as follows:
(0.83 - 0.8) / 0.02 = 1.5

Using a z-table, the probability of getting a z-score greater than 1.5 is 0.0668. Therefore, the answer is choice C.

A Sample of 400 Observations Will Be Taken from a Process