Math Is Fun Forum

bodie001

Member

Registered: 2010-01-05

Posts: 21

Help with Means

Instant dinner comes in packages with weights that are normally distributed with a standard deviation of 0.3oz.  If 2.3% of the dinners weigh more than 13.5oz, what is the mean weight?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi bodie001;

This one was made easy to solve, too easy to miss. From basic properties of the SNC you know that 1 sd from the mean on the right equals .3413 and 2 sd from the mean on the right = .4772. So a right tailed 2 sd is .5 + .4772 = .9772 . Which is 1 - .9772 = .0228 = 2.28 % or approximately 2.3% when rounded. The .0228 is the area you are interested in. This you can do now by yourself. Show me what you do here.

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

Hi Bobby,

Still trying to figure this out, but it is all greek to me.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi bodie001;

Since it looks like all your data has been rounded to .1 of a percent, we can say 2.28% = 2.3%

Think of it this way, if it is 2 sd's greater than the mean, and a sd is ,3 oz then it is .6 oz greater than the mean. So

13.5  - .6 = 12.9 oz. is the mean

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

Thank you...

One more that I am really struggling with:

Diameter of a pipe is normally distributed with a mean of 0.4 inch and a variance of 0.0004.  What is the probabilty that the diameter of a randomly selected pipe will exceed 0.44 inch. 

The book that I bought I can't understand how to apply and use any of the formulas.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi bodie001;

Do you know that the standard deviation is the square root of the variance?

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

No I didn't.  trying to get a handle on statistics before my class begins in about 2 weeks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi bodie001;

What book do you have?

Diameter of a pipe is normally distributed with a mean of 0.4 inch and a variance of 0.0004.  What is the probabilty that the diameter of a randomly selected pipe will exceed 0.44 inch.

So you are 2 standard deviations away. Can you take it from here?

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

I have the Nature of Math 11th edition.

I can almost see what you are doing, but still really have no idea.  I am done for when the spring semester starts.

thanks,

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi bodie001;

It is all in this graph. Look at it for a minute and if you still are stuck, tell me.
http://upload.wikimedia.org/wikipedia/c … iagram.svg

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

Hi bobby,

My computer is older and I can't open this link.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi;

Look at this for a little bit. Everything you need is right here.

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

I am looking at this and I can only guess that it's somewhere between 2.3% and the 15.9%

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi;

From the mean to 1 sd going right is .3413 and going from 1 sd to 2 sd's is .1359, now you know everything on the right of the mean is .5

Do you follow up to here?

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

Unfortunately I don't.  I think I will drop the course before it begins.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi;

Do you see the .3413 on the graph between 0 and 1?

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

Yes

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi;

That means that the area (probability) under the standard normal curve between 0 (the mean of a SNC) and 1 standard deviation to the right is .3413 Do you follow me? I will walk you through littla at a time, OK?

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

Yes so 2 deviations would be .1359?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Hi;

Yes, .1359 is the probability of between 1 standard deviation to 2 standadrd deviations. To find out the probability that something is between the mean and 2 standard deviations on the right you would add .3413 + .1359 = .4772. Do you follow this?

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

yes and if i change it to a precenage the answer would be 47.72%?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Yes, and what is the percentage of everything greater than 2 standard deviations from the mean.

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

97.7%?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help with Means

Nope, that is everything from the mean to 2 standard deviations from the mean. You want everything greater or on the right of 2 standard deviations.

---

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.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Help with Means

97.8%  and above?

i thought I was getting this.