Question

Nicole missed the lesson on normal distribution and needs to do her homework. Explain to Nicole how to use the mean and standard deviation of a normal distribution to determine the top 5% of the population.

Answer 1

@SarahEZZMcK

Do you know anyone who can help with this?

Answer 2

sounds like an emiprical rule approximation

Answer 3

I'm learning about Conditional Probablity

Answer 4

have you covered what a zscore is? (might be called a standard score)

Answer 5

No.

Answer 6

@aegidious @stonewoods @kag

Answer 7

hmm, then just knowing a mean and standard distribution might not be all that useful in determining the top 5%

the empirical rule is 64, 95, 99 giving us at best 2.5 % of the top

100 - 95
-------- = 2.5%


2

100-64
------- = 50-32 = 18% which is a far cry from 5%
2

Answer 8

so the thing is, the mean and sd can be used to determine a zscore, that can then be tabled up to find a probability

the table can also be used to find an appropriate zscore to work it backwards to find the value as well

Answer 9

\[z=\frac{x-mean}{sd}\]
if the z of .0500 is known than
\[mean+z(sd)=x\]defines the cutoff point for the top 5%

Answer 10

ok. So in order to find the answer we have to do everything backwards?

Answer 11

if you have a table, yes. if you have a ti83, no :)

Answer 12

I have a TI-84

Answer 13

Silver Edition. Will that work?

Answer 14

then to find the zscore, we would use the invnorm function under the distribution menu

Answer 15

2nd, VARS, invnorm: enter .95, since its a left tail measure.

invnorm(.05) would produce a negative z value, but due to symmetry of the curve, we would just ignore the sign.

we would still need to use that z value in the setup: mean + z(sd) to determine the cutoff point tho

Answer 16

Ummmm.... HUH?? Can you say that again. Except this time dumb it down a little.... or a lot. A lot is good too.

Answer 17

lets start with the basics, do you recall what a normal distibution curve looks like? and what the sd (standard deviation) measures on it?

Answer 18

Yes. A normal distribution curve looks a lot like a hill. and the (sd) measures the spread of normal distribution.

Answer 19

The spread of a normal distribution is controlled by the standard deviation, The smaller the standard deviation the more concentrated the data

Answer 20

good, the zscore tells us how many (sd) fit within a specific interval from the mean.

let say we have a mean of 'u' and have some value 'x', we want to know the distance that x is from the mean.



would you agree that the distance between them is simply (x - u)?