Question

A superstar major league baseball player just signed a new deal that pays him a record amount of money. The star has driven in an average of 110 runs over the course of his career, with a standard deviation of 31 runs. An average player at his position drives in 80 runs. What is the probability the superstar bats in fewer runs than an average player next year? Assume the number of runs batted in is normally distributed.

Answer 1

about 16.7%

Explanation:

An appropriate probability calculator can tell you the probability of being below 80 for the given normal distribution. The calculator shown below says it is about 0.167.

__

The corresponding z-value is ...

(x -μ)/σ = (80 -110)/31 = -30/31 ≈ -0.9677