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#1 2011-04-09 07:28:31

survival
Member
Registered: 2011-04-03
Posts: 655

Normal Distribution Using z-scores

Here's a good one for Sat.

A box of cereal contains 452 g with a standard deviation of 10.2 g. Find the probability
that a box contains more than 460 g. Assume a normal distribution. Use a x-score rounded to 2 decimal places.

Thanks.

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#2 2011-04-09 07:36:01

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

Sorry it's supposed to be 451 g. and the other number is :
no more than 453 g
my error

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#3 2011-04-09 08:09:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

Hi;

Is this what the question looks like?

A box of cereal contains 451 g with a standard deviation of 10.2 g. Find the probability
that a box contains no more than 453 g. Assume a normal distribution. Use a z-score rounded to 2 decimal places.

Is that 10.2 right?


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.

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#4 2011-04-09 08:12:12

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

Yes, that's exactly it.

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#5 2011-04-09 08:27:43

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

The formula for a z score is:

That means 453 gms is .1960 sd above the mean.

Now in the back of your text book or somewhere else they have given a table of z scores. Please use it and look up positive .196


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.

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#6 2011-04-09 08:35:34

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

I don't know if my answer was wrong yet, but I got .28. Above the mean is + and below is -. I will check the chart in my book for your answer.

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#7 2011-04-09 08:38:47

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

It shows .196 to be .475. Does that seem right?

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#8 2011-04-09 08:41:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

It is supposed to be .575 or about 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.

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#9 2011-04-09 08:47:57

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

.525 Is that the answer?
1 - .475 =.525

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#10 2011-04-09 08:49:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

Hi yes that is the answer. But that is the wrong z score.

Please check the table again for .196


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.

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#11 2011-04-09 09:05:27

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

.196 under z=.475
that is coming from a chart that says Areas Under the Standard Normal Curve.

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#12 2011-04-09 09:07:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

You are looking in the wrong spot.

Use the row that says .1 and go all the way over to the column that says .09

Make sure you are in the positve chart also.


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.

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#13 2011-04-09 09:08:05

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

good thing i don't work n a hospital. Patient would not fare well.

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#14 2011-04-09 09:10:08

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

You might some day. And I might be your patient. I want to live!!!!


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.

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#15 2011-04-09 09:13:58

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

that chart says .5753.

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#16 2011-04-09 09:14:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

Correct a mundo!

Now go

1 - .5753 = what?


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.

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#17 2011-04-09 09:25:00

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

.4247 ?

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#18 2011-04-09 09:33:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

Hi;

You are not sure?


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.

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#19 2011-04-09 09:44:04

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

no, i am just going by others i have worked and they all have.0 something after the answer. maybe multiply this my 100?

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#20 2011-04-09 09:49:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

Okay then round .4247 to the nearest hundredth and what do you get?


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.

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#21 2011-04-09 10:30:30

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

the answer has something to do with under the curve-to the right or left. I have never spent so much time on one problem.

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#22 2011-04-09 10:31:25

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

You are almost done please do the rounding I have asked for.

Do you need help with it?


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.

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#23 2011-04-09 10:49:32

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

I need to eat soon.
I am looking at one I worked last night or today and the only difference were the two numbers of grams.

A box of cereal contains 453 g with a standard deviation of 10.2 g. Find the probability that the box contains more than 461 g. Assume a normal deviation. Find the z-score for 461.
The final answer to that one is .0218.

Be back in a bit.

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#24 2011-04-09 11:02:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Normal Distribution Using z-scores

Okay, we will skip to the end then:

A box of cereal contains 451 g with a standard deviation of 10.2 g. Find the probability that a box contains no more than 453 g. Assume a normal distribution. Use a z-score rounded to 2 decimal places.

The area under the curve from 453 onwards is .4247

The question asks that the value is less than or equal to 453. That is all the area to the left. Now a SNC has a total area that equals 1.

If the area to the right is .4247 then the area to the left must be what is left that is just

1 - .4247 = ?


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.

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#25 2011-04-09 12:15:56

survival
Member
Registered: 2011-04-03
Posts: 655

Re: Normal Distribution Using z-scores

I am back, so back to thinking about that problem.

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