Question

Foot locker uses sales per square foot as a meaure of store productivity. sales are currently running at an annual rate of $406 per square foot. you have been asked by management to conduct a study of a sample of 64 foot locker stores.Assume the standard deviate in annual sales per square foot for the population of all 3400 Foot locker stores is $80.
a.) show the sampling distribution of x bar, the sample mean annual sales per square foot for a sample of 64 Foot locker stores.

b.)What is the probability that the sample mean will be within $15 of the population mean?

c.) Suppose you find a sample mean of $380. what is the probability of finding a sample mean of $380 or less? would you consider such a sample to be unusually low performing group of stores?

Answer 1

Answer and explanation:

Given : Foot locker uses sales per square foot as a measure of store productivity. sales are currently running at an annual rate of $406 per square foot. you have been asked by management to conduct a study of a sample of 64 foot locker stores.Assume the standard deviate in annual sales per square foot for the population of all 3400 Foot locker stores is $80.

To find :

a) Show the sampling distribution of x bar, the sample mean annual sales per square foot for a sample of 64 Foot locker stores.

By the central limit theorem also specifies that $\bar{x}$ will have the same expected value as the population mean, that is $E(\bar{x}) = 406$

The standard deviation of $\bar{x}$ is given by,

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt n}$

$\sigma_{\bar{x}}=\frac{80}{\sqrt {64}}$

$\sigma_{\bar{x}}=\frac{80}{8}$

$\sigma_{\bar{x}}=10$

b) What is the probability that the sample mean will be within $15 of the population mean?

The probability is  given by, $P(-15$

$P(\frac{-15}{\sigma_{\bar{x}}}$

$P(\frac{-15}{10}$

$P(-1.5$

From standard normal table,

$P(-1.5$

c) Suppose you find a sample mean of $380. what is the probability of finding a sample mean of $380 or less? would you consider such a sample to be unusually low performing group of stores?

$P(\bar{x}$

 $P(\bar{x}$

 $P(\bar{x}$

 $P(\bar{x}$

From standard normal table,

  $P(\bar{x}$