Given a sampling distribution of the sample mean that is normally distributed and has a mean of 30 and a standard deviation of 8, a sample mean of 40 corresponds to:
A) a z-value of -1.25
B) a z-value of +1.25
C) a z-value of +2.25
D) a sample size of 120
E) a sample size of 300

Question

Given a sampling distribution of the sample mean  that is normally distributed and has a mean of 30 and a standard deviation of 8, a sample mean of 40 corresponds to:
A) a z-value of -1.25 
B) a z-value of +1.25 
C) a z-value of +2.25 
D) a sample size of 120 
E) a sample size of 300

Quizplus · Accepted Answer

It can be solved using the formula z = (x̄ - μ) / (σ / √n). Plugging in the given values, we get z = (40 - 30) / (8 / √n). Solving for n, we get n = (8 / (40 - 30))² = 16. Therefore, the z-value corresponding to a sample mean of 40 is (40 - 30) / (8 / √16) = 1.25. So the answer is Choice B.

Given a Sampling Distribution of the Sample Mean That