Statistics
posted by Rodney on .
12. The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 94% of students now own a cell phone. Twenty five students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 15 who own a cell phone.
QUESTION: What is the probability that if you choose 40 people exactly 38 will have cell phones?

"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=1p=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 (ni=#of failures0, then
P(i)=C(n, i)p^{i}q^{ni}
and C(n, i) is the combination function, where
C(n,i)=n!/(i!(ni)!)
Example:
for n=40, i=38, p=0.99, q=0.03
I get P(38)=0.2206 
Sorry, for the example, p=0.97, q=0.03.