Historically the default rate on a certain type of commercia

Historically, the default rate on a certain type of commercial loan is 20 percent. If a bank makes 100 of these loans, what is the approximate probability that more than 24 will result in default? (Use the normal approximation. Round the z value to 2 decimal places.)

Solution

Here,

mean = n p = 100*0.20 = 20
standard deviation = np(1-p) = sqrt(100*0.20*(1-0.20)) = 4

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    24.5      
u = mean =    20      
          
s = standard deviation =    4      
          
Thus,          
          
z = (x - u) / s =    1.13      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.13   ) =    0.129238112 [ANSWER]