JustAnswer
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). 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).
|Mean arrival rate = 11 per minute |
|The arrivals follow a Poisson distribution |
|(a) μ = 11, x = 0 |
|P(x) = (e^-μ) * (μ^x) / x! |
|P(0) = (e^-11) * (11^0) / 0! = 1.67 * 10^-5 = 0.000017 |
|(b) μ = 11 |
|P(x ≤ 3) = P(0) + P(1) + P(2) + P(3) |
|= (e^-11) * (11^0) / 0! + (e^-11) * (11^1) / 1! + (e^-11) * (11^2) / 2! + (e^-11) * (11^3) / 3! |
|= 0.0049 |
|(c) μ = (1/4)(11) = 2.75 |
|μ = 2.75, x = 0 |
|P(x) = (e^-μ) * (μ^x) / x! |
|P(0) = (e^-2.75) * (2.75^0) / 0! = 0.0639 |
|(d) μ = (1/4)(11) = 2.75 |
|P(x ≥ 1) = 1 - P(0) = 1 - 0.0639 = 0.9361. |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.