Answer:
the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
Step-by-step explanation:
Let assume that n should represent the number of the students
SO,
can now be the sample mean of number of students in GPA's
To obtain n such that 
⇒ 
However ;

![E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D](https://tex.z-dn.net/?f=E%28x%5E2%29%20%3D%20D%5Cint%5Climits%5E4_2%20%282%2Be%5E%7B-x%7D%29dx%20%5C%5C%20%5C%5C%20%3D%20%5Cdfrac%7BD%7D%7B3%7D%5Be%5E%7B-4%7D%20%282e%5Ex%20x%5E3%20-3x%5E2%20-6x%20-6%29%5D%5E4__2%7D%7D%3D%2038.21%20%5C%20D)
Similarly;

⇒ 
⇒ 
⇒ 

∴ 
Now; 
Using Chebysher one sided inequality ; we have:

So; 
⇒ 
∴ 
To determine n; such that ;

⇒ 

Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
5/54 or approximately 0.092592593
There are 6^3 = 216 possible outcomes of rolling these 3 dice. Let's count the number of possible rolls that meet the criteria b < y < r, manually.
r = 1 or 2 is obviously impossible. So let's look at r = 3 through 6.
r = 3, y = 2, b = 1 is the only possibility for r=3. So n = 1
r = 4, y = 3, b = {1,2}, so n = 1 + 2 = 3
r = 4, y = 2, b = 1, so n = 3 + 1 = 4
r = 5, y = 4, b = {1,2,3}, so n = 4 + 3 = 7
r = 5, y = 3, b = {1,2}, so n = 7 + 2 = 9
r = 5, y = 2, b = 1, so n = 9 + 1 = 10
And I see a pattern, for the most restrictive r, there is 1 possibility. For the next most restrictive, there's 2+1 = 3 possibilities. Then the next one is 3+2+1
= 6 possibilities. So for r = 6, there should be 4+3+2+1 = 10 possibilities.
Let's see
r = 6, y = 5, b = {4,3,2,1}, so n = 10 + 4 = 14
r = 6, y = 4, b = {3,2,1}, so n = 14 + 3 = 17
r = 6, y = 3, b = {2,1}, so n = 17 + 2 = 19
r = 6, y = 2, b = 1, so n = 19 + 1 = 20
And the pattern holds. So there are 20 possible rolls that meet the desired criteria out of 216 possible rolls. So 20/216 = 5/54.
It’s 101 because 72 and -29 have a difference of 101