ssignment: Chapter 5 Section 6 SaveExit Subm uestions Exercise 05.19 Algorithmic

Question

ssignment: Chapter 5 Section 6 SaveExit Subm uestions Exercise 05.19 Algorithmic eBook KExerciae 5.49 (Alaorithmic)h Airline passengers arrive randomly and independently at the passenger-screening faoility at a major international airport. The mean arrival rate is 9 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). 0.0000 00045 00227 3 b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimala) c. Compute the probability of no arrivals in a 15-second period (to 4 decimals), d. Compute the probability of at least one arrival in a 15-second period (to 4 decimals). 00757 Hide Feedback Incorrect

Explanation / Answer

P(x) = (m^x * e^-m) / x!
m = 9/minute

a. P(0) = (9^0 * e^-9) / 0! = 0.0001

b. P(3 or fewer) = P(0) + P(1) + P(2) + P(3)
                 = m^0 * e^-m/0! + m^1 * e^-m/1! + m^2 * e^-m/2! + m^3 * e^-m/3!
                 = (9^0 * e^-9 / 0!) + (9^1 * e^-9 / 1!) + (9^2 * e^-9 / 2!) + (9^3 * e^-9 / 3!)
                  = 0.0212

c. If they get 9/minute, then the mean for 15 seconds is 2.25
P(0) = (2.25^0 * e^-2.25) / 0! = 0.1054

d. Subtract your answer in c. from 1

1 - P(0) = 1- 0.1054 = 0.8946

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