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 :)

Mr.Owl Oct 15, 2019

edited by
Guest
Oct 15, 2019

#1**0 **

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%

CPhill Oct 15, 2019

#2**0 **

Nice I got the first one correct, although I did it a little differently than you did.

Guest Oct 15, 2019

#5**+1 **

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**+1 **

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

#4**+2 **

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%

CORRECTED ANSWER !!!!

CPhill Oct 15, 2019

#6**+2 **

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%

CPhill Oct 15, 2019