Go to this website to view a \"histogram\" that displays the heights of most maj

Question

Go to this website to view a "histogram" that displays the heights of most major league baseball players from 1876 to 2012.

Question:

Suppose the distribution of player heights can be considered symmetric and mound-shaped with mean 73 inches and standard deviation 2.4 inches. Use the 68-95-99.7 rule to answer the following questions. This web site 68-95-99.7 rule graphically depicts the 68-95-99.7 rule and may help with the following questions.

a. What is the approximate percentage of the players that are taller than 68.2 inches?

____%

b. What is the approximate percentage of the players with heights between 75.4 inches and 77.8 inches?

_____%

c. If a particular player's height is equal to the 16th percentile of player heights, how tall (in inches) is the player?

____ inches

Note: read about the zany at-bat by the shortest player in baseball history by clicking here

http://www.baseball-almanac.com/charts/heights/heights.shtml

http://www.oswego.edu/~srp/stats/6895997.htm

Explanation / Answer

as we know that z score =(X-mean)/std deviation

a)therefore approximate percentage of the players that are taller than 68.2 inches =P(Z>(68.2-73)/2.4)

=P(Z>-2) =97.5%

b)approximate percentage of the players with heights between 75.4 inches and 77.8 =P(75.4<Z<77.8)

=P(2<Z<3)=(99.7-95)/2 =2.35%

c)for 16th percentile lies at -1 z score ; therefore correspondinjg height =73 -2*2.4=68.2

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