Given a sampling distribution of the sample mean, , that is normally distributed and has a mean of 30 and a standard deviation of 8, to which of the following does a sample mean of 40 correspond?
A) a z value of -1.25
B) a z value of +1.25
C) a sample size of 120
D) 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, to which of the following does a sample mean of 40 correspond?
A) a z value of -1.25 
B) a z value of +1.25 
C) a sample size of 120 
D) a sample size of 300

Quizplus · Accepted Answer

We can use the formula for z-score:

z = (x - μ) / (σ / sqrt(n))

Plugging in x = 40, μ = 30, σ = 8, and solving for n, we get:

1.25 = (40 - 30) / (8 / sqrt(n))

Simplifying, we get:

sqrt(n) = 10 / (8/1.25) = 15.625

Squaring both sides, we get:

n = 244.14

Since the sample size must be a whole number, the closest choice is D, a sample size of 300. However, the z-score corresponding to a sample mean of 40 is +1.25, so the correct answer is B.

Given a Sampling Distribution of the Sample Mean