Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 181 cm and a standard deviation of 6 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a. 169 cm and 193 cm b. 175 cm and 187 cm

Answer: Approximate 95% of the men between 169 cm and 193 cm and approximate 68%  the men between 175 cm and 187 cmStep-by-step explanation:[tex]\text{z score} = \dfrac {raw\ score - mean}{standard\ deviation}[/tex]We have, mean = 181 cm, standard deviation = 6cmNow, we have to find  the approximate percentage of the men between 169 cm and 193 cm and  175 cm and 187 cm[tex]z_1a = \dfrac{169 - 181}{6} = \dfrac {-12}6 = -2\\\\z_1b = \dfrac{193- 181}{6} = \dfrac {12}6 = 2\\\\z_2a = \dfrac {175 - 181}6 = \dfrac {-6}6 = -1\\\\z_2b = \dfrac{187 - 181}{6} = \dfrac {6}6 = 1[/tex]the empirical rule says:68 percent of data points for a normal distribution will fall within 1 standard deviation, 95 percent within 2 standard deviations, and 99.7 percent within 3 standard deviations.So, Approximate 95% of the men between 169 cm and 193 cm and approximate 68%  the men between 175 cm and 187 cm.