A population, with an unknown distribution, has a mean of 80 and a standard deviation of 7. For a sample of 49, the probability that the sample mean will be larger than 82 is:
A) 0.5228
B) 0.9772
C) 0.4772
D) 0.0228

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can find the probability that the sample mean is greater than 82. The standard error (SE) of the sample mean is the standard deviation divided by the square root of the sample size, which is 7 / sqrt(49) = 1. The Z-score for a sample mean of 82 is (82 - 80) / 1 = 2. Using the Z-table, the probability of a Z-score less than 2 is approximately 0.9772, so the probability of a Z-score greater than 2 is 1 - 0.9772 = 0.0228.

A Population, with an Unknown Distribution, Has a Mean of 80