Question

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 1

Answer:

Approximate 95% of the men between 169 cm and 193 cm and approximate 68%  the men between 175 cm and 187 cm

Step-by-step explanation:

$\text{z score} = \dfrac {raw\ score - mean}{standard\ deviation}$

We have,

mean = 181 cm, standard deviation = 6cm

Now, we have to find  the approximate percentage of the men between 169 cm and 193 cm and  175 cm and 187 cm

$z_1a = \dfrac{169 - 181}{6} = \dfrac {-12}6 = -2\\\\z_1b = \dfrac{193- 181}{6} = \dfrac {12}6 = 2\\\\z_2a = \dfrac {175 - 181}6 = \dfrac {-6}6 = -1\\\\z_2b = \dfrac{187 - 181}{6} = \dfrac {6}6 = 1$

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.