## Related questions with answers

A population and sample size are given. (a) Find the mean and standard deviation of the population. (b) List all samples (with replacement) of the given size from the population and find the mean of each. (c) Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. The minutes of overtime reported by each of the three executives at a corporation are 90, 120, and 210. Use a sample size of 3.

Solution

VerifiedGiven: $90, 120, 210$

$\begin{align*} n&=\text{Sample size}=3 \\ N&=\text{Population size}=3 \end{align*}$

The **mean** is the sum of all values divided by the number of values:

$\begin{align*} \overline{x}&=\dfrac{\sum_{i=1}^n x_i}{N} \\ &=\dfrac{\begin{matrix}90+120+210\end{matrix}}{3} \\ &=\dfrac{420}{3} \\ &=140 \end{align*}$

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