Statistics Help: Sample Means vs Individual

69.28

130.72





94.88





105.12



I would appreciate a quick check to see if I configured these correctly. For the top 2 because it is individual, I calculated it by:

First I looked up the z-score for 40% because half of 80% is .4 and the z-score closest I found was .3997, which corresponded with 1.28 and -1.28. Next I used the equation:

z-score= (x-mean) / standard deviation

So I did:

-1.28= (x-100) /24
-30.72= x-100
69.28= x (LOWER FOR INDIVIDUAL)

and

1.28= (x-100) /24
30.72= x-100
130.72= x (UPPER FOR INDIVIDUAL)

Next I used the equation:

z-score= (x-mean) / (standard deviation / sqrt of n) BUT X has line on top of it.

-1.28= (x-100) / (24 / sqrt of 36)
-1.28= (x-100) / (24 / 6)
-1.28= (x-100) / 4
-5.12= x-100
94.88= x (LOWER FOR SAMPLE MEANS)

(X still has line on top of it, I just don't know how to type that on here).

and

1.28= (x-100) / (24 / sqrt of 36)
1.28= (x-100) / (24 / 6)
1.28= (x-100) / 4
5.12= x-100
105.12= x (UPPER FOR SAMPLE MEANS)

(X still has line on top of it, I just don't know how to type that on here).

I think I have the hang of it, but I'm not quite sure yet as the x with and without the line on top of it is throwing me off if i calculated these right. Please let me know. I appreciate the help.

Looks good. I got the same results.

Thanks. Does the line on top of the x in the one formula and not in the other make no difference then?
​

---

x

or just x?

Sure thing! And if I'm understanding the question...the reason the second two calculations use x with the line above it is because x with a line above it is a sample mean. 4 is the standard error of the mean (i.e. the standard deviation of sample means). So in the second two calculations, we're looking at the distribution of the same means.

Thanks!