Tennis balls must meet certain specifications in order to be used in official toumament play. One of these specifications is rebound. For toumaments that are being played in high
altitude" conditions, a ball dropped from a height of 100 inches must rebound to a height
between 48 and 53 inches. A particular manufacturer has determined that the rebound heights
for balls it manufactures for high altitude conditions are normally distributed with standard
deviation of 11 inches. This manufacturer has a new process that allows it to set the mean
rebound of these balls
(3) If the manufacturer initially sets the mean rebound height to be 50 inches, what
proportion of balls produced by this method will not meet the tournament specifications
for rebound?
1
(b) Assume that the mean distance is set to 50 inches and that nine balls are independently
tested. What is the probability that no more than one of the balls fail to meet the rebound
specifications?
(C) What mean rebound height should the manufacturer use to maximize the proportion of
balls it sells that meet the specifications for high altitude rebound? Justify your answer.
(a) What is the maximum proportion of balls produced by this manufacturing process that
will meet the high altitude rebound specifications?