Question 560:

Asked on December 17, 2008

Tags: BINOMDIST , Binomial cdf , Compliment Rule

1

Answer:

No answer provided yet.

For this question we need to use the probabilities from the Binomial Distribution. There are published tables of binomial probabilities, however it is difficult to find one for a probability of .55 and sample size of 28, most stop at 20 and only have probabilities for every .10 values. We can calculate then by hand, but this will require 9 laborious and error prone calculations. The other alternative is to use Excel's built in binomial probability function =BINOMDIST() which will save a lot of hand calculations.

 

We'd enter the values =BINOMDIST(19,28,0.55,TRUE) where the parameters are 19: the number of people voting, 28: the total sample size, .55: the probability a person will vote and TRUE means to add up all the values from 0 to 19. This provides us with the Binomial cumulative distribution function (cdf).   Excel gives us the probability of 0.942245, BUT, this is the probability of 0 to 19 voting, we need the probability greater than 19 voting. Fortunately we can use the compliment rule of probability which states that the total probability must equal 1 and if we know the probability of an event, the probability of the event not occurring is 1 minus this value. So our result would be 1-.942245 = .057755, meaning there is around a 5.77% chance more than 19 registered voters will actually cast a ballot.