Suppose the average mileage rating in miles per gallon of a

Suppose the average mileage rating (in miles per gallon) of a particular model car is 28 mpg with a standard deviation of 8 mpg. A random sample of 64 cars of this model is selected.
What is the probability that the sample mean exceeds 30 mpg?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    30      
u = mean =    28      
n = sample size =    64      
s = standard deviation =    8      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132 [ANSWER]