Solve the problem. Round your answer to one decimal place, if necessary.
-The distribution of sample means for the ages of employees at a particular company for samples of 200 employees is normal with a mean of 40 and a standard deviation of 0.73. Suppose you take a random sample of 200 employees from the company and find that their mean age is 38.2. How many standard deviations is the sample mean from the mean of the distribution of sample means?
A)34.9 standard deviation(s)below the mean
B)2.5 standard deviation(s)below the mean
C)1.8 standard deviation(s)below the mean
D)2.5 standard deviation(s)above the mean

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Quizplus · Accepted Answer

To find how many standard deviations the sample mean is from the mean of the distribution of sample means, use the formula: (sample mean - mean of distribution) / standard deviation = (38.2 - 40) / 0.73 = -1.8 / 0.73 ≈ -2.5. This means the sample mean is 2.5 standard deviations below the mean of the distribution of sample means.

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