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December 20, 2014

December 20, 2014

Posted by **Rodney** on Thursday, April 19, 2012 at 12:00pm.

QUESTION: What is the probability that if you choose 40 people exactly 38 will have cell phones?

- Statistics -
**MathMate**, Thursday, April 19, 2012 at 12:57pm"Let X = the number of students in the sample of 15 who own a cell phone. "

does not seem to be relevant to the question.

Situation:

1. Each outcome is a Bernoulli trial, i.e. success (owns a cell phone) or failure (does not own one)

2. The probability of success is constant throughout the trials (p=0.94, q=1-p=0.06)

3. Every trial has equal probability as the others.

4. Every trial is independent of the others

5. There is a fixed number of trials (n=40)

Under these conditions, the probability can be modelled using the binomial distribution.

Let i=number of successes (n-i=#of failures0, then

P(i)=C(n, i)p^{i}q^{n-i}

and C(n, i) is the combination function, where

C(n,i)=n!/(i!(n-i)!)

Example:

for n=40, i=38, p=**0.99**, q=0.03

I get P(38)=0.2206

- Statistics - correction -
**MathMate**, Thursday, April 19, 2012 at 12:58pmSorry, for the example, p=0.97, q=0.03.

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