Question

A random sample of n = 9 scores is obtained from a population with μ = 50 and σ = 9. If the sample mean is M = 59, what is the z-score corresponding to the sample mean?

z = 3.00
z = 1.00    
z = 9.00
cannot determine without additional information

Answer 1

Sample mean from a sample of size n from a <i>normal</i> population with mean μ and σ has parameters N(μ,σ²/n)

Since n=9, σ=9, σ²/n=9, so the sample mean ~ N(50, 3²).

Z-score=((M-μ)/σ)=(59-50)/3=3