o The probability that an airplane is more than 45 minutes late on arrival is ab
ID: 2929988 • Letter: O
Question
o The probability that an airplane is more than 45 minutes late on arrival is about 15%. Let n-1, 2, 3, … represent the number of times a person travels on an airplane until the first time the plane is more than 45 minutes late. (a) Write a brief but complete discussion in which you explain why the geometric distribution would be appropriate. Write out a formula for the probability distribution of the random variable n (b) What is the probability that the third time a person flies is the first time the person is late by more the 45 minutes? (c) What is the probability that more than three flights are re- quired before a plane is more than 45 minutes late?Explanation / Answer
Q. 10 Probability that airplane is more than 45 minutes late = 0.15
(A) Here in this problem, we are asked to find number of times a person a person have to travel when he will be late for more than 45 minutes. So, As per the deifinition of geometric distribution, it entials the number of attempts require to get first succes. So, here first success is the first time the person will be late for flight for more than 45 minutes. So, yes, it is a geometric distribution.
Here p = 0.15
Pr(n) = (1-p)n-1p = 0.85n-1 * 0.15
(b) Here we have to find that it would be third time a person flies is the first time the person will be late.
Pr (n = 3) = 0.853-1 * 0.15 = 0.1084
(c) Here we have to find that probability that more than three flights are required before a plane is more than 45 minutes late.
Pr(n > 3) = 1 - [Pr(n=1) + Pr(n=2) + Pr(n =3) ]
= 1 - [ 0.15 + 0.85 * 0.15 + 0.852 * 0.15]
= 0.614
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.