A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is _____.
A) .5228
B) .9772
C) .4772
D) .0228

Question

Quizplus · Accepted Answer

To solve this problem, we will use the central limit theorem to approximate the sampling distribution of the sample mean. According to the central limit theorem, the sampling distribution of the sample mean will be approximately normal with a mean of 80 and a standard deviation of 7/√49 = 1.

We want to find the probability that the sample mean will be larger than 82:

P(X > 82) = P(Z > (82-80)/1) = P(Z > 2)

Looking at the standard normal distribution table, we can see that the probability of getting a Z-score larger than 2 is approximately 0.0228.

Therefore, the answer is D: 0.0228.

A Population Has a Mean of 80 and a Standard