Question

Height of men on a baseball team have a bell-shaped distribution with a mean of 180 cm and a standard deviation of 8 cm. using the empirical rule, what ist he approximate percentage of the men between the following values? a. 156 cm and 204 cm b. 172 cm and 188 cm Answer: ____% of men are between 156 cm and 204 cm ____% of men are between 172 cm and 188 cm

Answer 1

a. 99.7%

b. 68%

Explanation:

The empirical rule for approximately symmetrical and bell-shaped distributions states that:

68% of the data are among the values (means - sd) and (means + sd)

95% of the data are among the values (means - 2*sd) and (means + 2*sd)

99.7% of the data are among the values (means - 3*sd) and (means + 3*sd). So that,

68% of the data are among the values (180 - 8) = 172 and (180 + 8) = 188

95% of the data are among the values (180 - 16) = 164 and (180 + 16) = 196

99.7% of the data are among the values (180 - 24) = 156 and (180 + 24) = 204