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 GE 100)=

Solution

Here, the mean is

mean = 100*0.86 = 86
standard deviation = sqrt(n p (1-p)) = sqrt(100*0.86*(1-0.86)) = 3.469870315

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 100 - 0.5 = 99.5      
u = mean =    86      
          
s = standard deviation =    3.469870315      
          
Thus,          
          
z = (x - u) / s =    3.890635319      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   3.890635319   ) =    0.0000499911 [ANSWER]