The table below shows a frequency distribution for the heights of all Major League Baseball players from 1876-2012. (Source: www.baseball-almanac.com)

Height (inches) Frequency

63 to 65 73

66 to 68 1056

69 to 71 5006

72 to 74 7593

75 to 77 2903

78 to 80 291

81 to 83 11

The total number of people that played Major League Baseball between 1876 and 2012 is 16933.

The percentage of Major League Baseball players 6'0" or taller is 63.77%.

1. The mean height of men is 69.7 inches. Assume that the heights of men are normally distributed, with a standard deviation of 2.9 in.

a. 10% of men are taller than which height? Round your answer to 1 decimal place.

b. Find the percentage of men that are 6'0" or taller. Round your final answer to 2 decimal places.

(Grade breakdown: 3 for set up/work; 1 for answer; 1 for explanation)

c. How does the approximate percentage for the height of men 6'0" or taller (from the normal distribution) compare with the actual percentage of baseball players 6'0" or taller (indicated above)?

d. Based on your normal distribution calculation from part (b), approximately how many Major League Baseball players would you expect to be 6'0" or taller? Round your answer to the nearest whole number.