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# In the earlier exercise, a population and sample size are given. 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

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Given: $90, 120, 210$

$N*=\text{Number of samples}=27$

We need to determine all possible samples of size $3$ from the given population.

Next, we also need to determine the mean of each sample, which is the sum of the two data values divided by $3$.

$\begin{array}{ c c c | c } \text{1st data value} & \text{2nd data value} & \text{3rd data value} &\text{Mean} \\ \hline 90& 90& 90& \color{#4257b2}(90+90+90)/3=\color{black}90 \\ 90 & 90 & 120 & 100 \\ 90 & 90 & 210 & 130 \\ 90 & 120 & 90 & 100 \\ 90 & 120 & 120 & 110 \\ 90 & 120 & 210 & 140 \\ 90 & 210 & 90 & 130 \\ 90 & 210 & 120 & 140 \\ 90 & 210 & 210 & 170 \\ 120 & 90 & 90 & 100 \\ 120 & 90 & 120 & 110 \\ 120 & 90 & 210 & 140 \\ 120 & 120 & 90 & 110 \\ 120 & 120 & 120 & 120 \\ 120 & 120 & 210 & 150 \\ 120 & 210 & 90 & 140 \\ 120 & 210 & 120 & 150 \\ 120 & 210 & 210 & 180 \\ 210 & 90 & 90 & 130 \\ 210 & 90 & 120 & 140 \\ 210 & 90 & 210 & 170 \\ 210 & 120 & 90 & 140 \\ 210 & 120 & 120 & 150 \\ 210 & 120 & 120 & 180 \\ 210 & 210 & 90 & 170 \\ 210 & 210 & 120 & 180 \\ 210 & 210 & 210 & 210 \end{array}$

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