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# Ummmm

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1) In a standard normal distribution, what fraction of the data is between the mean and 0.6?

2) In a standard normal distribution, what percent of the data is between -0.4 and 0.4?

3) In a standard normal distribution, what percent of the data is between two and three standard deviations below the mean?

All help is appreciated :)

Oct 15, 2019
edited by Guest  Oct 15, 2019

#1
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1)   Here...I'm assuming that  .06   is a z score

The value  associated with a z score of  .06  =  .5239

The  mean will  have a z score of 0    .....of course.....the value associated with the mean  = .5000

So.....the percent of data falling between .5000  and .5239   =

[ .5239 - .5000]  =   ..0239  ≈    2.39%

Oct 15, 2019
edited by CPhill  Oct 15, 2019
#2
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Nice I got the first one correct, although I did it a little differently than you did.

Guest Oct 15, 2019
#3
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Sorry....I used the wrong value.....check my revised answer  !!!!

CPhill  Oct 15, 2019
#5
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I have a chart here and for 0.6 it says that 0.6 = .2257. Does that change anything? I am to use the chart that I have.

Guest Oct 15, 2019
#8
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I made the same mistake originally

z score for  0.6  =  .7257

But  we want the  score associated with  .06

This  is  .5239

CPhill  Oct 15, 2019
#10
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Oh dear, I seem to have made a typo. For question #1 it is asking for the data between the mean and 0.6. My apologies. Does this mean that your first answer was correct? The one that I also got the same answer for? Sorry again!

Guest Oct 15, 2019
#11
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Yeah....if it's supposed to be  0.6  the value is  .7257

So.....the % would be   [.7257 - .5000]  =  .2257 = 22.57%

CPhill  Oct 15, 2019
#4
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2) In a standard normal distribution, what percent of the data is between -0.4 and 0.4?

The z score value associated with .0.4  is .6554

The z score  value associated with -.0.4  is .3446

So.....the percent of data falling between these   is [ .6554 - .3446]  = .3108  =  31.08%

Oct 15, 2019
edited by CPhill  Oct 15, 2019
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Question #2 it is talking about .4 but in your answer, you found the z score for .04?

Guest Oct 15, 2019
#9
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CPhill  Oct 15, 2019
#6
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3) In a standard normal distribution, what percent of the data is between two and three standard deviations below the mean?

The percent of  data  falling between  two and three SDs   below the mean is the same  percent of data falling between two and three SDs  above the mean

The  percent   =   1.7%  between  2  and 2.5 SDs above the mean plus   .5 %  between 2.5 and 3 SDs  above the mean

So....the total %   =   [ 1.7  + .5 ] %  =   2.2%

Oct 15, 2019
#12
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Thank you very much for all of your help

Guest Oct 15, 2019
#13
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LOL!!!....I made more of a mess rather than giving correct answers   !!!!

CPhill  Oct 15, 2019