# Simple Binomial Distribution question (need clarification)

• Sep 3rd 2011, 01:58 AM
Paymemoney
Simple Binomial Distribution question (need clarification)
Hi
the following question i have done, but my answer is incorrect.

A company receives 70% of its orders over the internet. On a particular day it receives 32 independent orders. Calculate the probability that between 20 and 30 (both inclusive) of the orders are received over the internet?

This is what i have done

Pr(20 <= X <= 30) = Pr(X <=30) - Pr(X <= 20) = binomcdf(32,.7,30)-binomcdf(32,.7,20) = .7715

However when i done binomcdf(32,.7,30)-binomcdf(32,.7,19) = 0.864 which is the correct answer, but don't understand how this is correct.

according to the question if "both inclusive" shouldn't it be Pr(20 <= X <= 30) ?

P.S
• Sep 3rd 2011, 02:10 AM
CaptainBlack
Re: Simple Binomial Distribution question (need clarification)
Quote:

Originally Posted by Paymemoney
Hi
the following question i have done, but my answer is incorrect.

A company receives 70% of its orders over the internet. On a particular day it receives 32 independent orders. Calculate the probability that between 20 and 30 (both inclusive) of the orders are received over the internet?

This is what i have done

Pr(20 <= X <= 30) = Pr(X <=30) - Pr(X <= 20) = binomcdf(32,.7,30)-binomcdf(32,.7,20) = .7715

However when i done binomcdf(32,.7,30)-binomcdf(32,.7,19) = 0.864 which is the correct answer, but don't understand how this is correct.

according to the question if "both inclusive" shouldn't it be Pr(20 <= X <= 30) ?

P.S

You want:

Pr(20 <= X <= 30) = P(X=30)+...+P(X=20)

......... =[P(X=30)+..+P(X=0)] - [P(X=19)+...+P(X=0)]

......... = Pr(X <=30) - Pr(X <= 19)

CB
• Sep 3rd 2011, 02:27 AM
Paymemoney
Re: Simple Binomial Distribution question (need clarification)
but why is it from 19->0 shouldn't it be 20->0 if your saying including 20?
• Sep 3rd 2011, 03:53 AM
Plato
Re: Simple Binomial Distribution question (need clarification)
Quote:

Originally Posted by Paymemoney
but why is it from 19->0 shouldn't it be 20->0 if your saying including 20?

The complement of $P(X\ge 20)$ is $1-P(X< 20)=1-P(X\le 19)~.$
You want to include 20 and exclude 19 and below.
• Sep 3rd 2011, 04:32 AM
Paymemoney
Re: Simple Binomial Distribution question (need clarification)
i understand now thanks