Calculating Standard Scores for Sample Means Using the Central Limit Theorem

Question

Calculate the standard score ( z-score) of the given sample mean using the Central Limit Theorem.Round your answer to two decimal places.

μ= 36 and σ= 39; n=73; x bar = 38

Answer 1

The standardized z-score = (sample mean - population mean)/standard error of sample mean.

We are given the sample mean (xbar) = 38, the population mean (mu) = 36

The standard error of the sampling mean = population standard deviation (sigma) / square root of sample size (n) = 39 / square root (73) = 4.56

so z = (38 - 39) / 4.56 = -0.219