Normal Distribution Questions!

[snow]

A supplier contract calls for a key dimension of a part to be between 1.9 and 2.1 cm. That is, a part

will not be accepted if the dimension is out of the specified limits. The supplier has determined that the

standard deviation of its production process is 0.10 cm. The process is normally distributed.

(1) If the mean is 2.02 cm, what percentage of parts will meet the specification?

(2) If the mean is adjusted to 2.00 cm, what percentage of parts will meet the specification?

(3) If the mean is adjusted to 2.00 cm, the middle 95% of the parts produced will have dimension within

what limits? (Larger than? Smaller than?)

(4) If the mean is adjusted to 2.00 cm, how small must the standard deviation be to ensure that no more

than 2% of the parts are nonconforming (i.e. out of the specified limits above)?


I cannot figure out the meaning of normal distribution in this case. Do I need to use the density function to compute the probability? Its my first time to take the statistic class.

Thanks!

 

[Luke M]

This is beginning to sound like a homework problem...are you sure you're allowed to ask us?


If so, here's my two cents.

Normally distributed means that, statistically speaking, you have a bell shaped curve that is aligned over the middle (not favoring either side).

http://en.wikipedia.org/wiki/Normal_distribution


Knowing this, you can calculate what the percent chance of a part being 1x, 2x, or 3x the standard deviation from the mean. This lets you know how good your quality control is.

I believe this is the section you'll want to read up on:

http://en.wikipedia.org/wiki/Normal_distribution#Standard_deviation_and_confidence_intervals

 

[Sachin]

This is a homework problem. I just looked in my old statistics textbook and found a very similar problem, right down to the wording.


Snow, if you are truly a student, then you are wasting your money by posting the problems here. You will be better off puzzling through the problems yourself and learning how statistics work.

 

[SirJB7]

@Sachin

Hi!

Give a look to this other topic:

http://chandoo.org/forums/topic/how-to-get-random-variables-according-to-cumulative-probability

Regards!

 

[Hui]

@Snow

I agree with the comments made above about working through the problem so that you understand how the stats works.


However seeing how the problem is solved may assist this.


Q1. To work out what the probability of being between spec you need to work out the Cumulative Distribution below each point.

That is Cumm Dis below 2.1cm - Cumm Dis below 1.9cm

in Excel speak this will be

=NORMDIST(2.1,Mean,SD,TRUE)-NORMDIST(1.9,Mean,SD,TRUE)

=0.673075

=67.3075%


where:

Mean is a named range referring to the cell containing the Mean of 2.02

&

SD is a named range referring to the cell containing the Standard Deviation of 0.1


Q2. Adjust the cell containing the Mean to 2.00

=68.2689%


Q3. Here you need to workout what probability is below the two end points of the required distribution.

In this case you want 95% of the objects to be around the mean, that means there will be 2.5% below and 2.5% above the 95% range

To work this out using Excel

The lower boundary is : [code]=NORMINV(0.025,Mean,SD) = 1.804 cm

The upper boundary is : [code]=NORMINV(0.975,Mean,SD)

= 2.196 cm


Q4. I would setup this the same as question 3

where

Say A5: =NORMINV(0.02,Mean,SD)[/code]

Mean is set to 2.0

Then use Goal Seek, (Data, What If Analysis, Goal Seek)

Set Cell: A5

To value: 1.9

By changing Cell: SD cell

The SD cell should change to 0.048691

Check this with the upper end

=NORMINV(0.98,2,SD)[/code] which should display 2.1

and it does.


I would now lookup the NORMINV and NORMDIST functions in Excel help

and study what they do and how they work.


I am sure you'll quote this Post in your assignment as well!

 

[snow]

I have already finished it. Thank you though..

 

[snow]

Sachin,


Do not waste yout time on my post,please.

Thanks

 

[Hui]

Snow


Typically if you pose a question on a forum, you should keep an eye on it ever few hours or at least daily at a minimum.


In future please give us the respect to let us know that you have answered your own question, so that the few of us who did respond to you wont waste our time or can use our time to answer others questions.


Hui...