In order to reduce the lengths of baseball games MLB created

In order to reduce the lengths of baseball games, MLB created a rule that gives pitchers 12 seconds to pitch the ball to a batter. However, umpires have not routinely enforced this rule. Assume one particular pitcher\'s times are normally distributed with a mean of 14.88 seconds and a standard deviation of 2.5 seconds.

What is the probability that the first pitch in the third inning made by this pitcher will have a mean less than 14 seconds?

Solution

Mean( X-bar) = 14

Standard Deviation (SD) = 2.5

X = 14.88

z = ((X - (X-bar) ) / SD

   = ( 14.88 -14 ) / 2.5

   = 0.353

From z table,

Probability = 0.6368 Answer

The probability that the first pitch in the third inning made by this pitcher will have a mean less than 14 seconds = 0.6368.