SOLUTION: AT A COLLEGE, 1 OUT OF 4 STUDENTS ARE SOPHOMORES. IF 5 STUDENTS SURVEYED FIND THE A)MEAN B) VARIANCE C)STANDARD DEVIATION D) PROBABILITY THAT EXACTLY 3 ARE SOPHOMORES E)PROBA

Hi

1 OUT OF 4 STUDENTS ARE SOPHOMORES

p(sophmore) = p = .25  P(not sophmore) = q = .75

5 STUDENTS SURVEYED FIND: 

A)MEAN = 5*.25

B) VARIANCE = 5*.25*.75

C)STANDARD DEVIATION = sqrt(5*.25*.75)



Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = .25 & q = .75

nCx = 

D) PROBABILITY THAT EXACTLY 3 ARE SOPHOMORES = 10(.25)^3(.75)^2 = .0879

E)PROBABILITY THAT AT MOST 2 OR SOPHOMORES = P(0) + P(1) + P(2) 

P(0) + P(1) + P(2) =  .75^5 + 5*(.25)^1 *(.75)^4 + 10*(.25)^2 *(.75)^3 

P(0) + P(1) + P(2) = .2373 + .3955+ .2637 = .9844

F) AT LEAST 3 ARE SOPHOMORES = 1 -P(0) + P(1) + P(2) = .0156