Math Is Fun Forum

sparkeeuk

Member

Registered: 2011-10-20

Posts: 3

Standard Deviation problem

Hi, I wondered if someone on here could kindly help with one of my maths questions for my course as I can't seem to get my head round this and am hopin someone could put me in the right direction if possible, heres the question.......

The Lengths of pins produced by a machine follow a normal distribution with mean of 2.54cm and a standard deviation of 0.04cm. A pin is rejected if the length is less than 2.44cm or more than 2.60cm

a) What is the percentage of pins accepted

b) If it is decided that 2.5% of the pins are to be rejected because they are too short and 2.5% because they are too long, what is the new range of acceptable lengths

Would really appreciate any help on this

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Standard Deviation problem

Hi sparkeeuk;

a) We will do 2.44 first.

First you compute the z score:

So 2.44 is -2.5 sd from the mean.

Same thing for 2.6:

Now you are rejecting everything from -2.5 sd to - infinity and 2.5 to infinity.

This is done with a z score table which every stats book provides or with a calculator from the internet. Can you finish this one now?

---

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.

sparkeeuk

Member

Registered: 2011-10-20

Posts: 3

Re: Standard Deviation problem

Hi bobbym, thanks for taking time to have a look at this problem for me however I am still a bit confused for the second sum you done

has a total of 2.5 however I am reading it as 1.5

also for b) I look up on the table for say 2.5 which on mine relates to 0.9938 then I subtract 0.025 from it? and how do I find the new range from that?

Last edited by sparkeeuk (2011-10-21 01:46:42)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: Standard Deviation problem

hi sparkeeuk

yes, that does look like 1.5, rather than 2.5.  Oh bobbym, will you ever forgive me. 

Just checking out the MIF normal tables for the rest of the question.

OK. Got it.

http://www.mathsisfun.com/data/standard … table.html

This table starts at the middle and gives areas to the right of that, up to your calculated 'z' value.

So look for z = 1.5 and read off the probability of being between 0 and 1.5.

I make that 0.4332

So that's 43.32% to the right of the half way point.

Do a similar calculation for the LHS and add together the two answers.

To do part (b) you need to work that process in reverse.

2.5% will be a probability of 0.025 so the unknown 'z' value must give us 0.975 - 0.5 = 0.475 in the table.

What 'z' is that?

So

will enable you to get the upper limit.  Lower limit by symmetry.

Bob

Last edited by Bob (2011-10-21 03:22:12)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Standard Deviation problem

Hi sparkeeuk;

I remember a professor once telling me when I caught him making a mistake that he did those things on purpose to keep his students sharp. Even claimed that he wrote his books the same way. Of course, this is kaboobly doo. Yes, very good, it looks like 1.5 to me as well. Sorry.

To bob bundy;

To err is human, to forgive, divine.

Thanks for spotting that.

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: Standard Deviation problem

You're welcome. 

Does that mean you are divine then? 

Many of us have thought so for a while!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Standard Deviation problem

Does that mean you are divine then?

Nope! I never forgive anybody, anywhere, anytime. I just like that quote. I guess that makes me a monster.

That is me enjoying some warm tropical water.

That is me doing the rumbah with my date!

That is me being photographed outside Planet Hollywood, I was always shy around cameras.

Here I am doing La Traviatta by Verdi for my favorite gal. She is clearly being moved by my performance if I must say so myself.

So, we have a shy guy that loves Verdi, is fond of warm water and the Rumbah. Sounds pretty ordinary to me.

---

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.

sparkeeuk

Member

Registered: 2011-10-20

Posts: 3

Re: Standard Deviation problem

Thanks so much for your help took me a while to understand and was so relieved once it all clicked into place thanks again