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

P( Z < z ) = 0.15

using tables of normal distribution we will find a value of Z for probability of 0.15

z = -1.03

-1.03 = ( x - 4.6 ) / 0.82

x = 3.7554

$3.75 million