Question

For a sample of n = 30 scores, a score that is 6 points above the mean has a z-score of z = 1.50. What is the sample standard deviation?​ Group of answer choices

Answer 1

Answer:

4

Step-by-step explanation:

The z-score is calculated by the following formula

z=(x-μ)/σ

where

μ=Population mean

σ=Population standard deviation

If the z-score for a specific sample mean is discussed then z-score is computed as

z=xbar-μ/σxbar.

where

μ=Population mean

σxbar=Sample standard deviation

As the population mean and mean of sampling distribution of mean are equal so, μ is used in above equation.

Now, the z-score is given

1.5=xbar-μ/σxbar

σxbar=xbar-μ/1.5.

Also we know that z-score corresponds to a score that is 6 points above mean which means that xbar-μ=6.

σxbar=6/1.5

σxbar=4.

Thus, the required sample standard deviation is 4.