352 CHAPTER 6 Discrete Probability Distributions 19. Wendy's Drive-Through Cars arrive at Wendy's drive-through at a...

 

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352 CHAPTER 6 Discrete Probability Distributions 19. Wendy's Drive-Through Cars arrive at Wendy's drive-through at a rate of 0.2 car per minute between the hours of 11:00 PM. and 1:00 A.M. on Saturday evening. Wendy's begins an advertising blitz that touts its late-night service. After one week of advertising. Wendy's officials count the number of cars, X, arriving at Wendy's drive-through between the hours of 12:00 midnight and 12:30 A.M. at 200 of its restaurants. The results are shown in the following table: x (number of cars arriving) Frequency 1 4 2 5 3 13 23 25 28 25 27 21 15 4 5 6 7 8 9 10 11 12 13 14 15 16 (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. (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? 5 3 2 2 was u demo caval Prus reco the N 20 ( 352 CHAPTER 6 Discrete Probability Distributions 19. Wendy's Drive-Through Cars arrive at Wendy's drive-through at a rate of 0.2 car per minute between the hours of 11:00 PM. and 1:00 A.M. on Saturday evening. Wendy's begins an advertising blitz that touts its late-night service. After one week of advertising. Wendy's officials count the number of cars, X, arriving at Wendy's drive-through between the hours of 12:00 midnight and 12:30 A.M. at 200 of its restaurants. The results are shown in the following table: x (number of cars arriving) Frequency 1 4 2 5 3 13 23 25 28 25 27 21 15 4 5 6 7 8 9 10 11 12 13 14 15 16 (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. (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? 5 3 2 2 was u demo caval Prus reco the N 20 (

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a The pdf will be used to calculate the probabilites Following table shows the proba... View the full answer