You are a fast-food mogul and own 50 franchises of Longhorn Burgers and 40 franchises of Perfect Pitas. Suppose that the monthly revenue (in thousands of dollars) for every franchise is an i.i.d. random variable, with Longhorn Burgers revenues drawn from a distribution with (population) mean 20 and (population) standard deviation 4 and Perfect Pitas revenues drawn from a distribution with (population) mean 15 and (population) standard deviation 3. (Note that we have not assumed normality.) (a) In a given month, what is the approximate distribution of the sample average of the 40 franchises of Perfect Pitas? (b) In a given month, what is the approximate distribution of the sample average of monthly revenues at all 90 franchises? (Hint: Think separately about the sample average for the 50 Longhorn Burgers franchises and the sample average for the 40 Perfect Pitas franchises. Then, think about the overall sample average (for 90 franchises) as a linear combination of those two sample averages.)
You are a fast-food mogul and own 50 franchises of Longhorn Burgers and 40 franchises of Perfect Pitas. Suppose that the monthly revenue (in thousands of dollars) for every franchise is an i.i.d. random variable, with Longhorn Burgers revenues drawn from a distribution with (population) mean 20 and (population) standard deviation 4 and Perfect Pitas revenues drawn from a distribution with (population) mean 15 and (population) standard deviation 3. (Note that we have not assumed normality.) (a) In a given month, what is the approximate distribution of the sample average of the 40 franchises of Perfect Pitas? (b) In a given month, what is the approximate distribution of the sample average of monthly revenues at all 90 franchises? (Hint: Think separately about the sample average for the 50 Longhorn Burgers franchises and the sample average for the 40 Perfect Pitas franchises. Then, think about the overall sample average (for 90 franchises) as a linear combination of those two sample averages.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:You are a fast-food mogul and own 50 franchises of Longhorn Burgers and 40 franchises
of Perfect Pitas. Suppose that the monthly revenue (in thousands of dollars) for
every franchise is an i.i.d. random variable, with Longhorn Burgers revenues drawn
from a distribution with (population) mean 20 and (population) standard deviation 4
and Perfect Pitas revenues drawn from a distribution with (population) mean 15 and
(population) standard deviation 3. (Note that we have not assumed normality.)
(a) In a given month, what is the approximate distribution of the sample average of
the 40 franchises of Perfect Pitas?
(b) In a given month, what is the approximate distribution of the sample average of
monthly revenues at all 90 franchises? (Hint: Think separately about the sample
average for the 50 Longhorn Burgers franchises and the sample average for the
40 Perfect Pitas franchises. Then, think about the overall sample average (for 90
franchises) as a linear combination of those two sample averages.)
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