Major league baseball salaries averaged 326 million with a s

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in 2009. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million.

a) appox. 0

b) 0.9849

c) apprx. 1

d) 0.0151

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    3      
u = mean =    3.26      
n = sample size =    100      
s = standard deviation =    1.2      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.166666667      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.166666667   ) =    0.01513014 = 0.0151 [ANSWER, D]