Answer to Question #279929 in Statistics and Probability for TDJFUWE

Question

What proportion of this sample would you expect to have heights between 160 and 170 cm?

Answer 1

The heights of males are normally distributed with a mean of 165 centimeters and a standard deviation of 5 centimeters.

Use the Empirical Rule (“68 – 95 – 99.7 Rule”) to estimate the proportion of males whose height is between 160 and 170 cm

$$\mu=165, \sigma=5$$

$$P(160<X<170)=P(165-5<X<165+5)$$

$$=P(\mu-1\sigma<X<\mu+1\sigma)\approx0.6827$$

$68.27\%$