Question

Foot Locker uses sales per square foot as a measure of store productivity. Last year, the mean annual sales per square foot was $370 with a standard deviation of $38.54. Suppose you take a random sample of 64 Foot Locker stores operating last year. There is a 18% probability that the sample mean annual sales per square foot is at most $______.

a. 374.4321
b. None of the answers is correct
c. 365.5679
d. 334.5432
e. 405.4568

Answer 1

Answer: a. 374.4321

Explanation:

Taking the central limit theorem(number of samples is large) into consideration, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/(σ/√n)

Where

x = annual sales per square foot .

µ = mean annual sales per square foot

σ = standard deviation

n = number of samples

From the information given,

µ = $370

σ = $38.54

n = 64

The probability value is 18/100 = 0.18

Looking at the normal distribution table, the z score corresponding to the probability value is - 0.92

Therefore,

- 0.92 = (x - 370)/(38.54/√64)

x - 370 = - 0.9 × 4.8175 = 4.33575

x = 370 + 4.4321 = $374.4321