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 166 cm and a standard deviation of 5 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

a. 156 cm and 176 cm

b. 151cm and181cm

______ % of the men are between 156cm and 176cm.

­­­______ % of the men are between 151cm and 181cm. (DO NOT ROUND)

Solution

Let X be the heights of men on a baseball team

X is bell shaped with mean = 166 and std dev = 5 cm.

X is normal (166, 5)

a) 156<x<166

Convert 156 and 166 to z score

x = 156 ....> z = -2

x = 176   z=2

P(-2<z<0) = 0.9544

Or 95.44% of the men are between 156cm and 176cm.

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151 <x<181

|z|<3

P(|z|<3) = 0.9974

99.74% of the men are between 151cm and 181cm.