Consider the demand for Fresh Detergent in a future sales period when Enterprise Industries' price for Fresh will be $x_1=3\mathrm{.}87,$ the

average price of competitors' similar detergents will be $x_2=4\mathrm{.}18,$ and Enterprise Industries' advertising expenditure for Fresh will be $x_3$

$=\mathrm{.}00.$ A $95$ percent prediction interval for this demand is given on the following JMP output:

$($a$)$ Find and report the $95$ percent prediction interval on the output. If Enterprise Industries plans to have in inventory the number of

bottles implied by the upper limit of this interval, it can be very confident that it will have enough bottles to meet demand for Fresh in

the future sales period. How many bottles is this? If we multiply the number of bottles implied by the lower limit of the prediction

interval by the price of Fresh $($$$3\mathrm{.}87),$ we can be very confident that the resulting dollar amount will be the minimum revenue from

Fresh in the future sales period. What is this dollar amount? $($Round $95\frac{\%}{P}$I to $4$ decimal places and dollar amount and Level of

inventory needed to the nearest whole number.$)$

$($b$)$ Calculate a $99$ percent prediction interval for the demand for Fresh in the future sales period. Hint: $n=30$ and $s=0\mathrm{.}656.$ Optional

technical note needed. The distance value equals Leverage. $($Round your answers to $4$ decimal places.$)$