Nationwide the mean amount of sales each week at Lowes store

Nationwide, the mean amount of sales each week at Lowe’s store is normally distributed with a mean of $4.6 million with a standard deviation of $0.82 million. Lowe’s has decided to close 15% of its stores, and has chosen amount of sales as the criterion on which the decision will be based (they are going to close the 15% of the stores with the lowest sales). How much in sales does a store have to have in order to not be closed? (please express your answer in millions and round your answer to 2 decimal places)

Solution

X - Mean amount of sales per week is N(4.6, 0.82) (in million)

To be closed = 15% of the lowest

i.e. z score <-1.04

X score = -1.04(0.82) + 4.6

             = 3.7472

i.e where sales are below 3.7472 million those shops would be closed

or sales below 3.75 millions