Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Given:

μ = $3.26 million, averaged salary

σ = $1.2 million, standard deviation

n = 100, sample size.

Let x = random test value

We want to determine P (x>4).

Calculate z-score.

z = (x - μ) / (σ/√n) = (4 - 3.26) / (1.2/10) = 6.1667

From standard tables,

P (z<6.1667) = 1

The area under the distribution curve = 1.

Therefore

P (z>6.1667) = 1 - P (z<=6.1667) = 1 - 1 = 0

Answer: The probability is 0.