Question

Assume that airplanes land independently of one another on a particular runway. If there is an 8% chance that no airplanes land in an hour, what is the probability that six airplanes land in an hour?

A: 0.6188

B: 0.7351

C: 0.1515

D: 0.0288

Answer of (0.92)^6 = 0.6064 which is not an option

Answer 1

Solution:

We are given that: airplanes land independently of one another on a particular runway.

There is an 8% chance that no airplanes land in an hour.

So events are given on certain time period.

So number of outcomes happening in an hour follows Poisson distribution with parameter

We have:

P(No airplanes land in an hour) =8%
That is:

P(X =0)= 0.08

Using Poisson probability formula , we get:

Thus

Taking Log to the base e ( that is: Ln ) on both sides we get:

Thus

Now find : P( X = 6) =...........?

Thus correct option is: D. 0.0288