# Thread: How to find Standard Deviation?

1. ## How to find Standard Deviation?

In a population of men, their heights are normally distributed with a mean of 178 cm. If a man with a height of 184 cm is shorter than 20% of the population, determine the standard deviation of the population.
the answer is 8.3cm, but how do u do it with a graphic-calculator (TI series)?
if I use this formula, z=(x-mean)/standard deviation, the answer is 30, which is not the right answer, can anyone tell me why?
Thank you!

2. Originally Posted by wby
In a population of men, their heights are normally distributed with a mean of 178 cm. If a man with a height of 184 cm is shorter than 20% of the population, determine the standard deviation of the population.
the answer is 8.3cm, but how do u do it with a graphic-calculator (TI series)?
if I use this formula, z=(x-mean)/standard deviation, the answer is 30, which is not the right answer, can anyone tell me why?
Thank you!
Look up the z-score $\displaystyle z_{80}$ such that $\displaystyle p(z<z_{80})=0.8$ (he is taller than 80% of the population). My tables tell me that this is $\displaystyle 0.851$.

Now the z-score corresponding to $\displaystyle 184 \mbox{ cm}$ is:

$\displaystyle z=\frac{184-178}{\sigma}=0.841$

so $\displaystyle \sigma = 6/0.841 = 7.13 \mbox{ cm}$

RonL

3. Thank you, but do you know how to get the 0.841 on a graphic calculator?
(binomial pdf, normal pdf, normal inverse perhaps?)

4. Originally Posted by wby
Thank you, but do you know how to get the 0.841 on a graphic calculator?
(binomial pdf, normal pdf, normal inverse perhaps?)
No, but it is something like invnormaldis(0.8) that is inverse cumulative normal
of 0.8.

RonL

5. thank you!