Heights of men on a baseball team have a bellshaped distribu

*Heights of men on a baseball team have a bell-shaped distribution with a mean of 181 cm and a standard deviation of 6cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

a. ? % of the men are between 163 cm and 199 cm

b. ? % of the men are between 175 cm and 187 cm

Solution

a)

z-score for 163 = (163-181)/6 = -3

z-score for 175 = (199-181)/6 = 3

P( -3 <z < 3) = 0.99865- 0.00135 = 0.9973

Percentage of the men between 163 cm and 199 cm = 0.9973*100 = 99.73 %

b)

z-score for 163 = (175-181)/6 = -1

z-score for 175 = (187-181)/6 = +1

P( -1 <z < 1) = 0.84134-0.15866 = 0.68274

Percentage of the men between 163 cm and 199 cm = 0.68274*100 = 68.274 %