Let's look at the following example:

The on time arrival rate of planes landing at JFK is .89. What is the probabilty of taking a sample of 10 planes flying into JFK and all of them arrive on time?

We have a fixed number of trials of 10. (n=10)

There are only two possible outcomes for each trial: (on time or not on time)

There is a constant probability for on time arrival of .89 for each trial

There arrivals of each plane are indendent.

In that we meet the criteria for a binomial distribution we could use the following formula to solve:

P(X) = n!/x!(n-x)! (^x) (1 - )^n-x

P(10) = 10!/10!(10-10)! (.89¹⁰) (1 - .89)⁰

P(10) = .312

The probability of of all 10 flight out of 10 selected arrive on time is approximately 31.2%

Or you may use the computer to solve this problem for you. You could use Excel or google Binomial probability calculator to solve this.

Try the following problems and share them in this forum.

P (8 arrive on time)

P (5 arrive on time)

P (None arrive on time)