A sample of n = 36 scores is selected from a population with σ = 12.If the sample mean of M = 56 produces a z-score of z = +3.00,then what is the population mean?
A)50
B)52
C)54
D)56

Question

Quizplus · Accepted Answer

The population mean (μ) can be found using the formula for the z-score: $z = \frac{M - \mu}{\sigma / \sqrt{n}}$, where M is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the given values: $3 = \frac{56 - \mu}{12 / \sqrt{36}}$, solving for μ gives μ = 50.

A Sample of N = 36 Scores Is Selected from a Population