Question

Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. suppose a sample of 100 major league players was taken. find the approximate probability that the average salary of the 100 players exceeded $1 million.

Answer 1

Answer: The probability that the avg. salary of the 100 players exceeded $1 million is approximately 1.

Explanation:

Step 1: Estimate the standard error. Standard error can be calcualted by dividing the standard deviation by the square root of the sample size:

$SE=\frac{0.8}{\sqrt{100}}=\frac{0.8}{10} = 0.08$

So, Standard Error is 0.08 million or $80,000.

Step 2: Next, estimate the mean is how many standard errors below the population mean $1 million.

$\frac{1 - 1.5}{0.08}$

$=-6.250$

-6.250 means that $1 million is siz standard errors away from the mean. Since, the value is too far from the bell-shaped normal distribution curve that nearly 100% of the values are greater than it.

Therefore, we can say that because 100% values are greater than it, probability that the avg. salary of the 100 players exceeded $1 million is approximately 1.