Math Is Fun Forum

Spanky

Member

Registered: 2010-02-24

Posts: 62

Sampling Distribution

Ok, so my new math teacher isn't teaching our class anything and I could really use some help with the breakdown (with step by step instructions to help me understand how do work these problems in the future) of these problems .  I'm not sure what formulas to use and when.  Please help with this problem to start with!!

The breaking strength of untreated fabric is Normally distributed with mean 58 pounds and standard deviation 2.3 pounds.  The same type of fabric after treatment has Normally distributed breaking strength with mean 30 pounds and standard deviation 1.6 pounds.  A clothing manufacturer tests an SRS of 5 specimens of each fabric.
a) What is the probability that the mean breaking strength of the 5 untreated specimens exceeds 50 pounds?
b) What is the probability that the mean breaking strength of the 5 treated specimens exceeds 50 pounds?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sampling Distribution

Hi Spanky;

What is an SRS?

Here is some general info for solving a)

U = untreated, u = 58 and sd = 2.3

First find your z score:

So a mean of 50 is -3.4782 standard dev. from the mean. How do you turn that into a probability?
Do you know?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Spanky

Member

Registered: 2010-02-24

Posts: 62

Re: Sampling Distribution

Don't you look at Table A to find it?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sampling Distribution

Yes, that is one way using a table.

Since this is a one tail test I used this online calculator:

http://www.fourmilab.ch/rpkp/experiment … zCalc.html

Plug in -3.4782 and you get a probability of .000252 which is about one in 3962. Do you understand up till here? Did you get my numbers?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Spanky

Member

Registered: 2010-02-24

Posts: 62

Re: Sampling Distribution

I see how you got those numbers when i use your calculator, but we have to use the table in my class... so how would i go about this problem with the table? I'm not understanding what to do with the numbers you gave me from the online calculator...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sampling Distribution

What did you get from your table?

The numbers you will get from any table will be the same as the online calculator. Again, do you know how to read off -3.4782 from your chart? Most charts aren't as good as a calculator so you will have to round - 3.4782 to - 3.48.

Also I am doing general work for the typical problem like yours. But the questions are piling up. You have not answered as to what an SRS is and will it affect my calculation?

As soon as you can catch up to where I am in the problem then I can move on to the answer.

I see how you got those numbers when i use your calculator, but we have to use the table in my class... so how would i go about this problem with the table? I'm not understanding what to do with the numbers you gave me from the online calculator...

It appears you do not understand how to read the chart correctly. If not I will show you how, but I need to know where you are at before we go further.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Spanky

Member

Registered: 2010-02-24

Posts: 62

Re: Sampling Distribution

Ok well the chart says its 0.0003.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sampling Distribution

Hi;

That is correct! That is sufficiently close to .000253. That is the probabiliity of the event happening once.

The Prob. that that event happens all 5 times in 5 tries is just:

That is the answer for a) to the best of my knowledge, unless a SRS does something to alter my calculations. If not then you can try b). Please give it a try on your own. If you can't get it I will assist.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.