Exerclse $16-37$ Statlc $($Using Excel$)$

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A medical supply provider manufactures disposable N$95$ respirator masks and packages them into air$-$sealed boxes, with each box containing $200$ individual masks. Once a week, the company produces the masks and distributes them to several regional hospitals. The company also produces other types of masks and medical supplies that require the same resources. As a result, its production capacity for the N$95$ masks varies from week to week. The accompanying frequency distribution shows the weekly N$95$ mask production capacity from the previous $50$ weeks.

References

$\backslash$table$[[$Boxes of N$95$ masks,Frequency $($in weeks$)],[100,3],[150,8],[200,10],[250,17],[300,12]]$

During a pandemic, the company has difficulties predicting the demand for the N$95$ masks and can only speculate that, at minimum, the hospitals will need $170$ boxes of the masks on a weekly basis. After consulting with the local public health officials, the company believes that the hospitals will not require more than $400$ boxes of N$95$ masks per week, and the most likely demand would be about $200$ boxes each week.

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a$.$ Use Analysis ToolPak, with a seed of $1,$ to develop a Monte Carlo simulation with $500$ trials. What are the mean and standard deviation of the demand and production capacity?

Note: Round the final answers to four decimal places.

$\backslash$table$[[$Average demand,$178\mathrm{.}0000$