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.

90% of the time, an average of 10 randomly selected pitches by this pitcher will be more than how many seconds?

Solution

Mean( X-bar) = x

Standard Deviation (SD) = 2.5

X = 14.88

n =10

z for 90% = 1.645

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

=> 1.645 = ( 14.88 -x ) / (2.5/sqrt(10))

=> 1.3 = 14.88 -x

=> x = 14.88 - 1.3

=> x = 13.58 Answer