Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 6 - Normal Probability Distributions - 6-4 Sampling Distributions and Estimators - Basic Skills and Concepts: 4

Answer

No.

Work Step by Step

For the mean, the sampling distribution is basically a normal distribution with standard deviation $\frac{\sigma}{\sqrt n}$, whereas the found distribution is also basically a normal distribution, but has a standard deviation of $\sigma$. The two distributions have different standard deviations, therefore the answer is no.
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