The average monthly mortgage payment including principal and

The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is $180, find the probability that the mean mortgage payment of a random sample of 16 loans is less than $950?

Select one:

a. 0.43

b. 0.57

c. 0.24

d. 0.76

e. Cannot be determined

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    950      
u = mean =    982      
n = sample size =    16      
s = standard deviation =    180      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.711111111      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.711111111   ) =    0.238507693 = 0.24 [ANSWER, OPTION C]