The mean credit card debt for US household is 7115 with a st

The mean credit card debt for U.S. household is $7,115 with a standard deviation of $2,160. This mean is such a large value because of a few deeply indebted households. If a random sample of 50 U.S. households is selected, what is the approximate probability that the mean credit card debt for the sample exceeds $7,500?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    7500      
u = mean =    7115      
n = sample size =    50      
s = standard deviation =    2160      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.260352365      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.260352365   ) =    0.103771139 [ANSWER]