Question

Foot Locker uses sales per square foot as a measure of store productivity. Last year, the mean annual sales per square foot was $410 with a standard deviation of $54.38. Suppose you take a random sample of 36 Foot Locker stores operating last year. There is a 84% probability that the sample mean annual sales per square foot is at least $______.

Answer 1

Solution:-

Given that,

mean = = 410

standard deviation = = 54.38

n = 36

sample distribution of sample mean is ,

=

= 410

sampling distribution of standard deviation

=  / n = 54.38/ 36=

= 9.06

Using standard normal table,

P(Z > z) = 84%

= 1 - P(Z < z) = 0.84

= P(Z < z ) = 1 - 0.84

= P(Z < z ) = 0.16

= P(Z < z ) = 0.16

z = -0.99

Using z-score formula  

= z * +   

= -0.99*9.06+410

=$401