Normal Distribution Using z-scores

survival · 2011-04-09 07:28:31

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.

survival · 2011-04-09 07:36:01

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

bobbym · 2011-04-09 08:09:38

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?

survival · 2011-04-09 08:12:12

Yes, that's exactly it.

bobbym · 2011-04-09 08:27:43

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

survival · 2011-04-09 08:35:34

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.

survival · 2011-04-09 08:38:47

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

bobbym · 2011-04-09 08:41:45

It is supposed to be .575 or about that.

survival · 2011-04-09 08:47:57

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

bobbym · 2011-04-09 08:49:17

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

Please check the table again for .196

survival · 2011-04-09 09:05:27

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

bobbym · 2011-04-09 09:07:17

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.

survival · 2011-04-09 09:08:05

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

bobbym · 2011-04-09 09:10:08

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

survival · 2011-04-09 09:13:58

that chart says .5753.

bobbym · 2011-04-09 09:14:56

Correct a mundo!

Now go

1 - .5753 = what?

survival · 2011-04-09 09:25:00

.4247 ?

bobbym · 2011-04-09 09:33:52

Hi;

You are not sure?

survival · 2011-04-09 09:44:04

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

bobbym · 2011-04-09 09:49:17

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

survival · 2011-04-09 10:30:30

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.

bobbym · 2011-04-09 10:31:25

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

Do you need help with it?

survival · 2011-04-09 10:49:32

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.

bobbym · 2011-04-09 11:02:07

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 = ?

survival · 2011-04-09 12:15:56

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

Math Is Fun Forum

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

Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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

Re: Normal Distribution Using z-scores

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