Answer:
B
Explanation:
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The mean age of the employees at a large corporation is 35.2 years, and the standard deviation is 9.5 years. A random sample of 4 employees will be selected. What are the mean and standard deviation of the sampling distribution of the sample mean for samples of size 4 ? A. The mean is 35.2, and the standard deviation is 9.5. B. The mean is 35.2, and the standard deviation is 9.5/4. C. The mean is 35.2, and the standard deviation is 9.5/2. D. The mean is 35.2/4, and the standard deviation is 9.5/4. E. The mean is 35.2/2, and the standard deviation is 9.5/2.
Answer:
c. The mean is 35.2, and the standard deviation is 9.5/2
Explanation:
Using the central limit theorem, the mean and standard deviation of the sampling distribution are 35.2 and 9.5/2 respectively.
The mean of a sampling distribution according to the central limit theorem is equal to the mean of the population. Hence, mean of sampling distribution is 35.2Standard deviation of sampling distribution :
[tex] \frac{σ}{\sqrt{n}}[/tex]Hence,
Standard deviation = [tex] \frac{9.5}{\sqrt{4}} = \frac{9.5}{2}[/tex]Hence, the standard deviation of sampling distribution is 9.5/2
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