A department store will place a sale item in a special display for a one-day sal

Question

A department store will place a sale item in a special display for a one-day sale. Previous experience suggests that 27 percent of all customers who pass such a special display will purchase the item. If 1,320 customers will pass the display on the day of the sale, and if a one-item-per-customer limit is placed on the sale item, how many units of the sale item should the store stock in order to have at most a 1 percent chance of running short of the item on the day of the sale? Assume here that customers make independent purchase decisions.

Explanation / Answer

here mean number of items sold =np =1320*0.27=356.4

and std deviation =(np(1-p))1/2 =16.1298

for top 1% sales; at 99 percentile z=2.3263

hence corresponding sales for 1 percent chance of running short of the item on the day of the sale

=mean+z*std deviation =356.4+2.3263*16.1298 =393.92 ~ 394

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