4 According to statistics the probability that a student fin

4./ According to statistics the probability that a student finish college within 4 years is.8. We have a group of 15 students. a./ Find the formula for the exact probability that exactly probability that exactly 12 of the 15 students will finish college within 4 years. (What is the name of this distribution?)Don\'t try to calculate this exact probability. b./ Calculate the probability in question a./ using the table provided at the end of your test. c./ Let X be the number of students who will finish college within 4 years among the 15. Find the expected value and the standard deviation of X.

Solution

(a) X follows Binomial distribution with n=15 and p=0.8

P(X=x)=15Cx*(0.8^x)*(0.2^(15-x)) for x=0,1,2,...,15

So the exact probability is

P(X=12) = 15C12*(0.8^12)*(0.2^(15-12))

----------------------------------------------------------------------------------------------------------------

(b) The probability is

P(X=12) = 15C12*(0.8^12)*(0.2^(15-12)) = 0.2501389

----------------------------------------------------------------------------------------------------------------

(c)

expected value= n*p=15*0.8 =12

standard deviation =sqrt(n*p*(1-p)) =sqrt(15*0.8*0.2) =1.549193