# Normal distribution Q

Human heights are one of the many biological random variables that can be modelled by the normal distribution. The average height of Canadian women aged 18 and older is 163cm, while the average height for men is 177 cm. Assume the standard deviation for said Canadian men is 8cm.

a. What proportion of all men will be taller than 185cm?

b. What is the probability that randomly selected man will be between 170 and 185cm tall?

c. The height of the current PM is 188 cm tall. is this unusual height?

I got a and b figured out(except my answer for b is a bit different than answer key. I got 0.6519 as oppose to 0.6505. I think it should be acceptable though) But for C, I thought it's unusual height because it's outside of question b range which has 0.6 probability. But the answer key said no, it's usual height. Can anyone explain why?

• What if you are just visiting Canada on holiday? And what if the PM leaves Canada, becomes French, and then goes back to Canada? – wolfies Jun 1 '13 at 22:09

The height $188$ is $\frac{11}{8}$ standard deviation units up from the mean. If you look at standard normal tables, you will see that the probability that a normal is $1.3375$ standard deviation or more units up from the mean is about $0.0845$. That really doesn't qualify as unusual. Particularly if we double and note that being $1.375$ or more standard deviation units away from the mean has probability about $0.169$, definitely not at all unusual.