Question

A population has a mean of 500 and a standard deviation of 50. A sample of 40 will be taken and the sample mean x̄ will be used to estimate the population mean. Assume that the population is infinite.

What is the standard deviation of x̄?

a. 1.25
b. 7.91
c. 40
d. 50

Answer 1

Answer on question #53372, Math / Statistics and Probability

Question A population has a mean of 500 and a standard deviation of 50. A sample of 40 will be taken and the sample mean $\bar{x}$ will be used to estimate the population mean. Assume that the population is infinite. What is the standard deviation of $\bar{x}$?

Solution Deviation of sample is related to deviation of population as

$\bar{\sigma}=\frac{\sigma}{\sqrt{n}}=\frac{50}{\sqrt{40}}\approx 7.9$

Hence, answer is b.7.91

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