Normal Distribution Using z-scores

survival · 2011-04-09 12:41:10

1 - .4247 = .5753. Isn't that too much?

bobbym · 2011-04-09 13:54:04

Nope! That is the answer.

survival · 2011-04-09 13:56:16

okay, i am going to type it in and see what happens.

bobbym · 2011-04-09 13:57:12

Whoa! Hold it you must round that answer to the nearest 100th.

survival · 2011-04-09 14:45:37

I typed in the .575 and it didn't take it. I have one more try.

bobbym · 2011-04-09 14:46:41

Try .58

survival · 2011-04-09 15:37:35

ok, i will try that one. It is homework, not a test, but it does tell me the answer when i get it wrong after a couple of tries.

bobbym · 2011-04-09 16:04:53

Okay I will wait.

survival · 2011-04-09 17:35:35

Well, it let me keep it open for one more try. You know how the chart on the positive side has spaces between with no answer on some lines? In my text, it has a chart with numbers that skip like that.
If I know what lies between there, I bet the answer is there. It has me fascinated. I solved another one kind of like it and only got the answer correct, because I'd seen one done in class. It's that space between the z and the A that holds the key.

survival · 2011-04-09 17:37:11

Math is interesting after all, if i could just understand it.

bobbym · 2011-04-09 18:19:26

Hi;

Are you saying that was not the correct answer!

I am interpreting the question as everything to the left of .1960 standard deviations on a SNC.

survival · 2011-04-10 00:31:59

Sorry, i posted in wrong place. The answer is:
0.421.
What is confusing me is that when you divide the mean by standard deviation, it usually gives you the right answer. This one did not. There was a difference. I worked it the right way and so did you and I cannot explain the difference in answers. I will be back later and post the way the answer is shown.

bobbym · 2011-04-10 04:13:58

Hi survival;

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.

I find the problem awful. And I hate the way they carelessly teach students to round off answers and data in a totally unpredictable way.

First thing the problem does not state what the the mean is. We have to assume the mean is 451 gms. To get .421 we take the area between 451 and 453 and subtract that from 1 / 2. Ugggggh!!!!

Also it appears that they want you to round up .196 to .2 z scores. Using either .19 or .2 is highly inaccurate. I am forced to think have they ever heard of linear interpolation!

survival · 2011-04-10 11:23:03

hello,
Yes, they teach to round sometimes and sometimes don't mention it. Most confusing!

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.

z = x - mean
_____________
standard deviation

They did not show the numbers except after it was already divided.
"The area between z = 0 and z = 0.2 is 0.079.
The area to the right of z is 0.421. (Round to nearest thousandth)
Therefore the probability that a box of cereal contains more than 453 g. is approximately 0.421."
I still don't know why all three of us came up with a different answer, although the only answer they wanted was mechanical-theirs.
Look at the answer. Why couldn't the answer have been 0.079? What caused the difference in that and the final answer? I have no clue. Where did the difference in the two numbers come from?

bobbym · 2011-04-10 14:19:19

Hi survival;

Actually it is more like .077 see what I mean.

The area to the right of z is actually .4222

Now here is where it gets weird. No more than 453 gms means everything that is less than or equal to it. From 0 to 453. That area is .5777

survival · 2011-04-10 15:23:27

I guess I am in for a rough quiz if they are like that. "No more than" is confusing, it could mean anything.

bobbym · 2011-04-10 15:25:56

Hi;

Maybe there will not be anymore like that. Do you have a T.A. that you can ask about this particular problem?

survival · 2011-04-11 13:27:32

hello bobbym,
I asked and was given these figures:
x= the box of cereal
z = x - x with level over it
z= 453 -451 divided by 10.2
1960, 784, 314
z=-20
.5-.079 then the answer is .421

bobbym · 2011-04-11 13:55:46

Hi;

That is what I figured. The wording of the problem is ambiguous at best. It even tripped me up. No wonder people hate math.

Math Is Fun Forum

#26 2011-04-09 12:41:10

Re: Normal Distribution Using z-scores

#27 2011-04-09 13:54:04

Re: Normal Distribution Using z-scores

#28 2011-04-09 13:56:16

Re: Normal Distribution Using z-scores

#29 2011-04-09 13:57:12

Re: Normal Distribution Using z-scores

#30 2011-04-09 14:45:37

Re: Normal Distribution Using z-scores

#31 2011-04-09 14:46:41

Re: Normal Distribution Using z-scores

#32 2011-04-09 15:37:35

Re: Normal Distribution Using z-scores

#33 2011-04-09 16:04:53

Re: Normal Distribution Using z-scores

#34 2011-04-09 17:35:35

Re: Normal Distribution Using z-scores

#35 2011-04-09 17:37:11

Re: Normal Distribution Using z-scores

#36 2011-04-09 18:19:26

Re: Normal Distribution Using z-scores

#37 2011-04-10 00:31:59

Re: Normal Distribution Using z-scores

#38 2011-04-10 04:13:58

Re: Normal Distribution Using z-scores

#39 2011-04-10 11:23:03

Re: Normal Distribution Using z-scores

#40 2011-04-10 14:19:19

Re: Normal Distribution Using z-scores

#41 2011-04-10 15:23:27

Re: Normal Distribution Using z-scores

#42 2011-04-10 15:25:56

Re: Normal Distribution Using z-scores

#43 2011-04-11 13:27:32

Re: Normal Distribution Using z-scores

#44 2011-04-11 13:55:46

Re: Normal Distribution Using z-scores

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