Solve the problem. Round your answer to one decimal place, if necessary.
-The distribution of sample means for monthly employee income at a particular company for samples of 70 employees is normal with a mean of $5921 and a standard deviation of $219. You take a random sample of 70 employees from the company and find that their mean monthly income is $5668. How many standard deviations is the sample mean from the mean of the distribution of sample means?
A)1.2 standard deviation(s)below the mean
B)1.2 standard deviation(s)above the mean
C)9.7 standard deviation(s)below the mean
D)253 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: $Z = \frac{\bar{x} - \mu}{\sigma}$, where $\bar{x}$ is the sample mean, $\mu$ is the mean of the distribution of sample means, and $\sigma$ is the standard deviation of the distribution of sample means. Plugging in the given values: $Z = \frac{5668 - 5921}{219} = \frac{-253}{219} \approx -1.2$. This means the sample mean is 1.2 standard deviations below the mean of the distribution of sample means.

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