Question

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 178 cm and a standard deviation of 7 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?

a. What ​% of the men are between 157 cm and 199 cm?

b. What % of the men are between 171 cm and 185 cm?

Answer 1

Let X follows normal distribution with mean = = 178 cm and standard deviation = = 7 cm

a) Empirical rule:

i) About 68% data lies in between 1 standard deviation from the mean.

ii)  About 95% data lies in between 2 standard deviation from the mean.

iii) About 99.7% data lies in between 3 standard deviation from the mean.

a) Here we want to find K such that

Therefore we use (iii) rule.

So that about 99.7% of the men are between 157 cm and 199 cm.

b) Next we want to find k such that  

Therefore we use (i) rule.

So that about 68% of the men are between 171 cm and 185 cm.