Solve the problem. Round your answer to one decimal place, if necessary.
-The distribution of sample means for a group of test scores for samples of 100 scores is normal with a mean of 61.2 and a standard deviation of 1.7. Suppose you take a sample of 100 test scores and find that the mean is 59.3.
How many standard deviations is the sample mean from the mean of the distribution of sample means?
A)1.9 standard deviation(s)below the mean
B)1.1 standard deviation(s)below the mean
C)11.2 standard deviation(s)below the mean
D)1.1 standard deviation(s)above the mean

Question

Quizplus · Accepted Answer

The number of standard deviations the sample mean is from the mean of the distribution of sample means is calculated by the difference between the sample mean and the distribution mean, divided by the standard deviation: (61.2 - 59.3) / 1.7 = 1.9 / 1.7 ≈ 1.1. This indicates the sample mean is 1.1 standard deviations below the mean of the distribution of sample means.

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