Given a normally shaped distribution with a μ = 100 and a σ = 16, a sample of 36 individuals is randomly selected. The mean of the sample was 107. The z-score for the sample mean would be _______.
A) +2.62
B) -2.62
C) +.44
D) -.44

Question

Quizplus · Accepted Answer

The formula for calculating the z-score is:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (107 - 100) / (16 / sqrt(36))
z = 7 / (16 / 6)
z = 2.625
z ≈ 2.62

Therefore, the z-score for the sample mean is +2.62.

Given a Normally Shaped Distribution with a μ = 100