It is known that 86 of freshmen students receive a scholarsh

It is known that 86% of freshmen students receive a scholarship. A class is randomly selected of 100 students what is the probability that all of them receive a scholarship? Using the binomial normal approximation with continuity correction find:

(give your answer to three decimal places)

P(x>100)=

Solution

Mean ( np ) =86
Standard Deviation ( npq )= 100*0.86*0.14 = 3.4699
Normal Distribution = Z= X- u / sd                   

P(X > 100) = (100-86)/3.4699
= 14/3.4699 = 4.0347
= P ( Z >4.035) From Standard Normal Table
= 0.00002734 ~ it is zero