Question 1087753
Question:
1. Twenty-three percent of Ole Miss students are from out of state.  In a random sample of 6 students, what is the probability that at least 2 of them are from out of state?(round to whole number) 
a. 42%        b. 7%           c. 28%           d. 64%         e. none of these
2. For the problem above what is the expected value of x.
a. 4.2        b. 2.7           c. 1.4           d. .5         e. none of these
 
Solution:
Since the probability is known and constant (large population), the binomial distribution can be used to model the situation.
p=0.23
n=6
(1) At least two student from out-of-state.
P(x)=C(n,x)p^(x)*(1-p)^(n-x)
=1-C(6,0)(0.23)^0*(0.77)^6-C(6,1)(0.23)^1*(0.77)^5
=1-0.2084-0.3735
=0.4180

(2) Expected value of x 
Expected value of x (in a binomial distribution)
=np
=6*0.23
=1.38