Restaurant car arrival frequency x (number of cars arriving) 1 2 234 3 5 6 7 8 9 10 11 12 13 14 15 16 12 16 Print Frequency 5 4 14 24 25 31 24 26 21 RS23203 15 5 Done Cars arrive at a certain restaurant's drive-through at a rate of 0.2 cars per minute between the hours of 11:00 P.M. and 1:00 AM on Saturday evening. The restaurant begins an advertising blitz that touts its late-night service. After one week of advertising, the restaurant's officials count the number of cars, X, arriving at the restaurant's drive-through between the hours of 12:00 midnight and 12:30 A.M. for 204 of its restaurants. The results are shown in the following table. Use the table to answer parts (a) through (c) to the right. (a) Construct a probability distribution for the random variable X, assuming it follows a Poisson process with A-0.2 and t-30. This is the probability distribution of X before the advertising. Remember that x= 0,1,2,3...16. (b) Compute the expected number of restaurants that will have 0 arrivals, 1 arrival, and so on. (c) Compare these results with the number of arrivals after the advertising. Does it appear the advertising was effective? Why? (Determining the advertising campaign effectiveness requires comparing the expected outcomes with the observed data. This can be done by comparing the observed total number of arrivals to the expected total number of arrivals.)
Restaurant car arrival frequency x (number of cars arriving) 1 2 234 3 5 6 7 8 9 10 11 12 13 14 15 16 12 16 Print Frequency 5 4 14 24 25 31 24 26 21 RS23203 15 5 Done Cars arrive at a certain restaurant's drive-through at a rate of 0.2 cars per minute between the hours of 11:00 P.M. and 1:00 AM on Saturday evening. The restaurant begins an advertising blitz that touts its late-night service. After one week of advertising, the restaurant's officials count the number of cars, X, arriving at the restaurant's drive-through between the hours of 12:00 midnight and 12:30 A.M. for 204 of its restaurants. The results are shown in the following table. Use the table to answer parts (a) through (c) to the right. (a) Construct a probability distribution for the random variable X, assuming it follows a Poisson process with A-0.2 and t-30. This is the probability distribution of X before the advertising. Remember that x= 0,1,2,3...16. (b) Compute the expected number of restaurants that will have 0 arrivals, 1 arrival, and so on. (c) Compare these results with the number of arrivals after the advertising. Does it appear the advertising was effective? Why? (Determining the advertising campaign effectiveness requires comparing the expected outcomes with the observed data. This can be done by comparing the observed total number of arrivals to the expected total number of arrivals.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:Restaurant car arrival frequency
x (number of
cars arriving)
1
2
3
4
6
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8
9
10
11
12
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14
15
16
Print
Frequency
SALLES NENS I NO NOM
5
4
14
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31
24
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21
15
5
2
3
2
3
Done
1
<
Cars arrive at a certain restaurant's drive-through at a rate of 0.2 cars per minute between the hours of 11:00 P.M. and 1:00 A.M on Saturday evening. The
restaurant begins an advertising blitz that touts its late-night service. After one week of advertising, the restaurant's officials count the number of cars, X,
arriving at the restaurant's drive-through between the hours of 12:00 midnight and 12:30 A.M. for 204 of its restaurants. The results are shown in the
following table. Use the table to answer parts (a) through (c) to the right.
(a) Construct a probability distribution for the random variable X, assuming it follows a Poisson process with λ=0.2 and t-30. This is the probability
distribution of X before the advertising. Remember that x= 0,1,2,3,...,16.
(b) Compute the expected number of restaurants that will have 0 arrivals, 1 arrival, and so on.
(c) Compare these results with the number of arrivals after the advertising. Does it appear the advertising was effective? Why?
(Determining the advertising campaign effectiveness requires comparing the expected outcomes with the observed data. This can be done by comparing
the observed total number of arrivals to the expected total number of arrivals.)
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