The bank of Connecticut issue Visa and MasterCard credit car

The bank of Connecticut issue Visa and MasterCard credit cards. It is estimated that the balances on all Visa credit cards have a mean of $845 and a standard deviation of $270. What is the probability that a randomly selected Visa Card issued by the bank has a balance between $1,000 and $1,400?

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    1000      
x2 = upper bound =    1400      
u = mean =    845      
          
s = standard deviation =    270      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    0.574074074      
z2 = upper z score = (x2 - u) / s =    2.055555556      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.717041162      
P(z < z2) =    0.980087312      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.263046151   [ANSWER]