The mean Credit Score score of 65 applicants who were applyi

The mean Credit Score score of 65 applicants who were applying for car loans was 520 with variance of 225.About how many applicants scores were between 470 and 570?

Solution

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    470      
x2 = upper bound =    570      
u = mean =    520      
          
s = standard deviation =    15      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -3.333333333      
z2 = upper z score = (x2 - u) / s =    3.333333333      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.00042906      
P(z < z2) =    0.99957094      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.999141879

Thus, those between 470 and 570 are

65*0.999141879 = 64.94422216 or 65 [AROUND ALL!]