The Student Room Group

S1 - Normal Distribution. Explanation please?

Hi. I've stumbled across this question where I'm just stuck on how they managed to derive an answer. Can anyone help me out here?

A geologist is analysing the size of quartz crystals in a sample of granite. She estimates that
the longest diameter of 75% of the crystals is greater than 2 mm, but only 10% of the crystals
have a longest diameter of more than 6 mm.
The geologist believes that the distribution of the longest diameters of the quartz crystals can

be modelled by a normal distribution.
(a) Find the mean and variance of this normal distribution.
Reply 1
Have you been provided the actual sample analyse? I'm not sure how you're expected to model said distribution and derive the mean and variance from it without?
Reply 2
Solve these simultaneous equations;

6μ=1.28σ6 - \mu = 1.28\sigma
2μ=0.67σ2 - \mu = -0.67\sigma
Reply 3
Right, sorry I was being thick a moment ago!

If the distribution referred to is a standard normal distribution the mean will be 0 and the variance 1 (I recall). The question is vague however, and 'normal distribution' can refer to several things.

If however that is the full of extent of the question and materials given I don't think they'd be expecting anything else as derivation isn't allowed by that alone really.
Reply 4
Yep I had a look at the working out behind this and it is rather straight forward. It'd be more accurate to say that I can't visualise the distribution curve.

Maybe I'm being stupid here but is there a reason why it's using the negative sign highlighted? I'm bothered by the fact that I'll be calculating an answer without understanding what I'm working out exactly.
doji how did you get 1.28 and -0.67?
Reply 6
ok 1.28 because its closes to 0.9 area value, (1 - 0.1) = 0.9

-0.67 because its (1 - 0.75) = 0.25 ... but we use 0.75 as 0.25 is not on the table, and we just make it negative as we'll flip it over anyway so closest to 0.75 is z=0.67, but -0.67 as its on the left side of the mean etc, just draw the graph to imagine it.
Reply 7
I think I finally understand it somewhat now... could you just have a look at my diagram to make sure I'm calculating the correct sections?

We're essentially comparing that 10% and that 25% section?
Thanks!

Ergh... I've hit another mental block. Okay I understand that in order to get the 25% side, we calculate the 75% to the left and minus that from 1 which gives the value 0.68

What good does changing that value 0.68 to negative? How exactly does it flip the diagram? Am I now calculating 25% to from the left hand side because of the flip, or something else.
Reply 8
thirdrate
A couple of points.

Your diagram is wrong. You cannot have 75% above the mean.
The 75% area must start to the left of the mean.

-0.68 is correct because...

the table tells you that
75% lie below mean+0.68
so
75% lie above mean-0.68


75% lie below the mean? I'm sorry but I don't fully understand. :frown:

The way I'm looking at the diagram.

75% are over 2mm, 10% are over 6mm.
I'll treat the middle point as 50%, so there are 25% over the middle and 40% over for the other figure. The complete left hand side would be 0%

Bleh, sorry dude. These values don't help much as I'm not even sure what section of the diagram I'm meant to be figuring out in the first place. I'll take another stab at creating it in my mind.
Reply 9
This was the only other alternative idea I could come up with, for some reason I feel that the higher mm would be on the right hand side rather than the left hand side though.
Reply 10
Thirdrate, I just want to say that I really appreciate your help with this, sorry for not understanding so far.

Right am I trying to calculate the little 10% block at the end, or the 90% before it?
Same goes for the 75% above 2mm, or the 25% under 2mm.

Would it be possible to draw a diagram on how you view this? It'd certainly help me understand things more clearly.
Reply 11
thirdrate
Sorry, I don't know what you are trying to calculate. Only you know that. :smile:
As for the diagrams...I'm guessing you didn't see my last post.


Yep I just saw. I've refined my diagram somewhat now based on yours.

Looks like I was calculating the wrong thing the entire time... :s-smilie:

In order to calculate that 10% grey block at the end. I was using 1-90% at the front. Don't know whether this was possible however.

Then I tried calculating the 75% grey block by the similar method but had to use the table as there was 25% on the other side.

I'll have to look more indepth into the whole thing once more. Cheers for your help, Rep coming your way tomorrow ^^
Reply 12
how do know when to subtract the value from one?