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

0.1667

Step-by-step explanation:

Given that:

Average / mean runs (m) = 110 runs

Standard deviation (σ) = 31 runs

Number of runs driven in by an average player in his position = 80

The probability the superstar bats in fewer runs than an average player next year will be the :

P(x < 80)

Zscore = (x - mean) / σ

Zscore = (80 - 110) / 31

Zscore = - 30 / 31

Zscore = - 0.9677419

P(Z < 0.9677419) = 0.1666 ( from z probability calculator)

= 0.1667

x/3-10=8

x/3=18

x=48