Question

Major league baseball salaries averaged a $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What is the approxiamate probability that the mean salary of the 100 players was less than $3.0 million?   

Answer 1

Mean, = $3.26 million

Standard deviation, = $1.2 million

Sample size, n = 100

For sampling distribution of mean,

P( < A) = P(Z < (A - )/)

= = $3.26 million

= ​​​​​​

=

= 0.12

P(mean salary of the 100 players was less than $3.0 million) = P( < 3.0)

= P(Z < (3 - 3.26)/1.2)

= P(Z < -2.17)

= 0.0150