The average score of all golfers for a particular course has

The average score of all golfers for a particular course has a mean of 67 and a standard deviation of 4. Suppose 64 golfers played the course today. Find the probability that the average score of the 64 golfers exceeded 68.

A) 0.3707

B) 0.0228

C) 0.4772

D) 0.1293

Solution

RIGHT TAILED AREA          
          
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    68      
u = mean =    67      
n = sample size =    64      
s = standard deviation =    4      
          
Thus,          
          
z =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132 = 0.0228 [OPTION B, ANSWER]