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.
Answer:
20
Step-by-step explanation:
Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.
<h3>What is the binomial distribution formula?</h3>
The formula is:


The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem, we have that:
- There are 6 students, hence n = 6.
- There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.
The probability of one quote being chosen at least two times is given by:

In which:
P(X < 2) = P(X = 0) + P(X = 1).
Then:



Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.

0.0328 = 3.28% probability that at least 2 of them choose the same quote.
More can be learned about the binomial distribution at brainly.com/question/24863377
Answer:
Dom(gof)=Dom(f)={1,3,4}.
(gof)(1)=g{f(1)}=g(2)=3.
(gof)(3)=g{f(3)}=g(5)=1.
(gof)(4)=g{f(4)}=g(1)=3.
∴gof={(1,3),(3,1),(4,3)}.
no, it is constant for a while then changes at 90gallons