d. Find the 25-th and the 95-th percentiles of the distribution of revenue when A = 2. [The p-th percentile is that value of R, R_p, such that P(R < R_p) = p]. e. Compute the level of advertisement expenditure to ensure that the probability of revenue being larger than $110,000 is 0.95. Show an explanatory graph.
d. Find the 25-th and the 95-th percentiles of the distribution of revenue when A = 2. [The p-th percentile is that value of R, R_p, such that P(R < R_p) = p]. e. Compute the level of advertisement expenditure to ensure that the probability of revenue being larger than $110,000 is 0.95. Show an explanatory graph.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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please answer the question in the attached picture with work shown, thanks!
#3 D,E
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A firm's revenue, in $1000, is estimated by the equation R = 100 + 20A + X, where A, the
advertisement expenditure in $1000s is known (non-random), and X - N(0, 900) for any value of A.
a. Draw a sketch of the relationship E(R|A) and advertisement expenditure, where A varies from 0 to
5 (Note: This is a conditional expectation, E(R|A) = 100 + 20A)
b. Compute the probability that the revenue is greater than $110,000 if advertisement expenditure is
equal to $2000, P(R > 110 A = 2). Draw a sketch to illustrate your calculation.
c. Compute the probability that revenue is greater than $110,000 if advertising expenditure equals
$3000, P(R > 110 | A = 3).
d. Find the 25-th and the 95-th percentiles of the distribution of revenue when A = 2. [The p-th
percentile is that value of R, R_p, such that P(R < R_p) = p].
e. Compute the level of advertisement expenditure to ensure that the probability of revenue being
larger than $110,000 is 0.95. Show an explanatory graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6dd8cd7d-ead2-463e-8d97-a89a3fd16a37%2F5a8c0299-0099-4a89-a214-dd7be3b3b388%2F9mg2xwe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3
A firm's revenue, in $1000, is estimated by the equation R = 100 + 20A + X, where A, the
advertisement expenditure in $1000s is known (non-random), and X - N(0, 900) for any value of A.
a. Draw a sketch of the relationship E(R|A) and advertisement expenditure, where A varies from 0 to
5 (Note: This is a conditional expectation, E(R|A) = 100 + 20A)
b. Compute the probability that the revenue is greater than $110,000 if advertisement expenditure is
equal to $2000, P(R > 110 A = 2). Draw a sketch to illustrate your calculation.
c. Compute the probability that revenue is greater than $110,000 if advertising expenditure equals
$3000, P(R > 110 | A = 3).
d. Find the 25-th and the 95-th percentiles of the distribution of revenue when A = 2. [The p-th
percentile is that value of R, R_p, such that P(R < R_p) = p].
e. Compute the level of advertisement expenditure to ensure that the probability of revenue being
larger than $110,000 is 0.95. Show an explanatory graph.
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