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 $5587 and a standard deviation of $220. You take a random sample of 70 employees from the company and find that their mean monthly income is $5837. How many standard deviations is the sample mean from the mean of the sampling distribution?
A)1.1 standard deviation(s)above the mean
B)250 standard deviation(s)above the mean
C)1 standard deviation(s)above the mean
D)9.5 standard deviation(s)above the mean

Question

Quizplus · Accepted Answer

The number of standard deviations the sample mean is from the mean of the sampling distribution is calculated using the formula: $Z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the mean of the sampling distribution, $\sigma$ is the standard deviation of the sampling distribution, and $n$ is the sample size. Plugging in the given values: $Z = \frac{5837 - 5587}{220/\sqrt{70}} \approx 1.1$.

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