# How to find Standard Deviation?

• August 10th 2007, 10:59 PM
wby
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!
• August 10th 2007, 11:51 PM
CaptainBlack
Quote:

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 $z_{80}$ such that $p(z (he is taller than 80% of the population). My tables tell me that this is $0.851$.

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

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

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

RonL
• August 11th 2007, 12:06 AM
wby
Thank you, but do you know how to get the 0.841 on a graphic calculator?
(binomial pdf, normal pdf, normal inverse perhaps?)
• August 11th 2007, 12:08 AM
CaptainBlack
Quote:

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
• August 11th 2007, 05:42 PM
wby
thank you!