The owner of a meat market has an assistant who has determined that the weights of roasts are normally distributed,with a mean of 3.2 pounds and standard deviation of 0.8 pounds.If a sample of 25 roasts yields a mean of 3.6 pounds,what is the Z-score for this sample mean?
A)−2.50
B)2.50
C)−0.50
D)None of these choices.

Question

Quizplus · Accepted Answer

The formula for calculating the Z-score for a sample mean is:

Z = (x̄ - μ) / (σ / sqrt(n))

where
x̄ = sample mean
μ = population mean
σ = population standard deviation
n = sample size

Substituting the given values, we get:

Z = (3.6 - 3.2) / (0.8 / sqrt(25))
Z = 0.4 / 0.16
Z = 2.5

Therefore, the Z-score for the sample mean of 3.6 pounds is 2.5, which corresponds to choice B.

The Owner of a Meat Market Has an Assistant Who