Question

A sample of n = 36 from a population of μ = 50 and σ = 18 has a mean M = 47. What is the z-score for the sample means?

a) -1.67
b) -1.33
c) -0.67
d) -0.33

Answer 1

For a sample with a mean of 47 from a population with a mean of 50 and standard deviation of 18, when the sample size is 36, the z-score for the sample mean is calculated to be -1.

Step-by-step explanation:

The z-score for the sample mean is calculated using the formula:

z = (M - μ) / (σ / √n)

Where M is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

By substituting the given values:

z = (47 - 50) / (18 / √36)

z = (-3) / (18 / 6)

z = -3 / 3

z = -1

This finds the z-score for sample means.