For a specific year Americans spent an average of 7112 for b

For a specific year, Americans spent an average of $71.12 for books. Assume the variable is normally distributed. If the standard deviation of the amount spent on books is $8.42, find these probabilities for a randomly selected American. Put answer in percent form.

a. He or she spent more than $60 per year on books.

Solution

RIGHT TAILED AREA          
          
We first get the z score for the said value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    60      
u = mean =    71.12      
n = sample size =    1 (just one individual)      
s = standard deviation =    8.42      
          
Thus,          
          
z =    -1.320665083      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.320665083) =    0.906693469 [ANSWER]