Question

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 166 cm166 cm and a standard deviation of 6 cm6 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?a. 148148 cm and 184184 cm b. 160160 cm and 172172 cm

Answer 1

Answer:

a) 89%; b) 68%

Step-by-step explanation:

We know that a mean $\mu=166$ and a standard deviation is $\sigma=6.$

a) Notice that 148 and 184 are each exactly 3 standard deviation away from the mean:

$\frac{148-166}{6}=-3\\ \frac{184-166}{6}=3$

So, we get that at least $(1-(\frac{1}{3} )^2)=89%$ of the men has a height between 148 cm and 184 cm.

b) Notice that 160 and 172 are exactly 1 standard deviation away from the mean.

$\frac{160-166}{6}=-1\\\\\frac{172-166}{6}=1$  

By the empirical rule , 68% of the men has a height between 160 cm and 172 cm.