Foot Locker uses sales per square foot as a measure of store productivity. Sales are currentlyrunning at an annual rate of $406 per square foot (the Wall Street Journal, March 7, 2012).You have been asked by management to conduct a study of a sample of 64 Foot Lockerstores. Assume the standard deviation in annual sales per square foot for the population ofall 3400 Foot Locker stores is $80.a. Show the sampling distribution of x, the sample mean annual sales per square foot fora sample of 64 Foot Locker stores.b. What is the probability that the sample mean will be within $15 of the populationmean?c. Suppose you find a sample mean of $380. What is the probability of finding a samplemean of $380 or less? Would you consider such a sample to be an unusually lowperforming group of stores?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 (the Wall Street Journal, March 7, 2012).
You have been asked by management to conduct a study of a sample of 64 Foot Locker
stores. Assume the standard deviation in annual sales per square foot for the population of
all 3400 Foot Locker stores is $80.
a. Show the sampling distribution of x, 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 an unusually lowperforming group of stores?
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