Question

Heights of men on a baseball team have a bell-shaped distribution with a mean of 184 cm and a standard deviation of 8 cm.
Using the empirical rule what is the approximate percentage of the men between the following values
a. 160 cm and 208cm
b. 168 cm and 200 cm

Answer 1

Answer:

Given that:

Heights of men on a baseball team have a bell-shaped distribution with a mean of 184 cm and a standard deviation of 8 cm.

MEAN = 184

STANDARD DEVIATION = 8

a) 160 cm and 208cm

P(160<X<208) =

For x = 160, z = (160 - 184) / 8 = -24/8 = -3 and for x = 208, z = (208 - 184) / 8 = 24/8 = 3

Hence P(160 < x < 208) = P(-3 < z < 3) = [area to the left of z = 3] - [area to the left of -3]

P(160 < x < 208) = 0.9974

b) 168 cm and 200 cm

P(168<X<200) =

For x = 168 , z = (168 - 184) / 8 = -16/8 = -2 and for x = 200, z = (200 - 184) / 8 = 16/8 = 2

Hence P(168 < x < 200) = P(-2 < z < 2) = [area to the left of z = 2] - [area to the left of -2]

P(168 < x < 200) = 0.9544