Stepwise Descriptive Statistics Learning

Which of the following is a quality criterion for appraising a systematic review?
Question 2 options:

results presented as a meta-analysis
providing details about the search strategy
data synthesis provided in a Forest plot
inclusion of only randomized controlled trials

I want to apply to a university where the 25th /75th percentiles for the SAT Math are 490 / 620 respectively, but I am curious how would I find the mean and the standard deviation assuming that the data is normally distributed? I know that we are talking about the middle 50th-percentile and $z_{0.25}=620$ and $z_{0.75}=490$

Assume the average of laptop computer is $875 with a standard deviation of $65. The following data represent the prices of a sample of laptops at an electronics store. Calculate the z-score for each of the following prices.

Use the standard normal table to find the z-score that corresponds to the given percentile. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score.
$P_{80}$
The z-score that corresponds to $P_{80}$ is ...
(Round to two decimal places as needed.)

When looking at effect size, Cohen's dis 2.03. What does this indicate for effect size?
It does not pass the effect size test
The effect size is small
The effect size is medium
The effect size is large

For a z-test for one proportion, a possible effect size measure is
$(p–p_0)/\sqrt{p_0(1-<!--\; -\; -->p_0)}$
where $P_0$ is the null value and p is the true population proportion, which can be estimated using the sample proportion. What is the relationship between this effect size and the z-test statistic for this situation? Does the effect size fit the relationship "Test statistic = Size of effect x Size of study"? If not, explain why not. If so, show how it fits. What would be a reasonable way to estimate this effect size?

A random variable X is normally distributed with $\mathrm{\mu <!--\; \mu \; -->}=60$ and $\mathrm{\sigma <!--\; \sigma \; -->}$ = 3. What is the value of 2 numbers a,b so that $P(X=a)=P(X=b)$.
The solution is $a=60$ and $b=65$.
However, I do not know how to come up with that answer. As far as I understand $P(X=a)$ and $P(X=b)$ have to be both 0 since you always have to give a range e.g. $P(a<X)$. Moreover if I insert the values 60 and 65 in the formula $Z=(X-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->})/\mathrm{\sigma <!--\; \sigma \; -->}$ than I would end up with 0,1.667 and z-scores 0.5, 0.952 respectively.

How do you find the domain & range for $f(x)=2\cos <!--\; \; -->(4x+\mathrm{\pi <!--\; \pi \; -->})-<!--\; -\; -->1$?

What is the z-score of sample X, if $n=36,\mathrm{\mu <!--\; \mu \; -->}=12.3,\text{St.Dev}=21,{\mathrm{\mu <!--\; \mu \; -->}}_X=18.5$?

What is the z-score of sample X, if

Automorphism group of a graph = Automorphism group of that graph's adjacency matrix?
Is automorphism group (or set) of a graph G equal to the automorphism group (or set) of adjacency matrix of G?
Example: $G_1,G_2$ are separate graphs where $G_1^{\mathrm{\pi <!--\; \pi \; -->}}=G_2$ and $G={\stackrel{¯<!--\; ¯\; -->}{G}}_1\cup <!--\; \cup \; -->{\stackrel{¯<!--\; ¯\; -->}{G}}_2$. Also, $\mathrm{\pi <!--\; \pi \; -->}$ swaps only 2 vertices of $G_1$, say, it swaps $k^{th}$ vertex with $(k+1{)}^{th}$ vertex.
So, the adjacency matrix of $G_1\ne <!--\; \ne \; -->$ the adjacency matrix of $G_2$.
We will have this dissimilarity in G also.
G is made of 2 non equal matrices of ${\stackrel{¯<!--\; ¯\; -->}{G}}_1,{\stackrel{¯<!--\; ¯\; -->}{G}}_2$. There are only two dissimilar columns/ rows. They are $k^{th}$, $(k+n{)}^{th}$ and $(k+1{)}^{th},(k+1+n{)}^{th}$ vertex. Remaining all pairs of rows/columns (i,i+n) are same where $i\ne <!--\; \ne \; -->k,k+1$
Now, consider a permutation σ of G that swaps $k^{th}$ vertex of Gwith $(k+1+n{)}^{th}$ vertex of G. Note that, $k^{th}$ vertex is in $G_1$ and $(k+1+n{)}^{th}$ vertex is in $G_2$.
here, the adjacency matrix of $G^{\mathrm{\sigma <!--\; \sigma \; -->}}\ne <!--\; \ne \; -->$ the adjacency matrix of G.
So, Automorphism group of a graph $\ne <!--\; \ne \; -->$Automorphism group of that graph's adjacency matrix.
Is it correct?
This post is the source of my argument.
If A is a matrix and π is an automorphism of A, then $A^{\mathrm{\pi <!--\; \pi \; -->}}=A$.

What distinguishes meta-analysis from meta-synthesis?
A) Meta-analysis uses a systematic approach; meta-synthesis does not use a systematic approach.
B) Meta-analysis is used for qualitative studies; meta-synthesis is used for quantitative studies.
C) Meta-analysis uses only published evidence; meta-synthesis uses both published and unpublished evidence.
D) Meta-analysis is used for quantitative studies; meta-synthesis is used for qualitative studies.

What is the length of the bar needed to represent 75 kilometers( in centimeters)?
In a bar graph, 1 centimeter represents 30 kilometers. What is the length of the bar needed to represent 75 kilometers( in centimeters)?

A distribution has a standard deviation of ${\displaystyle \sigma =8}$. How do you find the z-score below the mean by 8 points?

Are Linear Complexes and Simple Graphs the same thing?
I refer to the background of the notion of Linear complex by A. A. Zykov in the article entitled "General properties of Linear Complexes"
A Linear complex (or simplex complex) is a finite set L for which the set $(L{)}^2$ of all pairs is split into non- intersection parts: $(L{)}^2=K+\stackrel{¯<!--\; ¯\; -->}{K,}$ with the following conditions:
(I) Two pairs, which differ only in the order of the elements, belongs to one and the same part.
(II) The pairs of equal elements belongs to $\stackrel{¯<!--\; ¯\; -->}{K}$.
The number e(L) of elements of the complex L is called its order.
The elements A and B of L are called adjacent $(A\mathrm{\omega <!--\; \omega \; -->}B)$, if the pair of them belongs to K, and not adjacent $(A\stackrel{¯<!--\; ¯\; -->}{\mathrm{\omega <!--\; \omega \; -->}}B)$, if it belongs to $\stackrel{¯<!--\; ¯\; -->}{K}.$. The condition I expresses the symmetric property of the sign ω, the condition II its anti- reflexiveness.
The complexes $L_1$and $L_2$are equal ($L_1$=$L_2$if they consist of the same elements and if any two elements which are adjacent in $L_1$ are adjacent in $L_2$, and conversely.
The complementary complex to L is that complex $\stackrel{¯<!--\; ¯\; -->}{L}$which consists of the same elements but in which any two distinct elements which are adjacent in L are not adjacent in $\stackrel{¯<!--\; ¯\; -->}{L}$, and conversely.
Now, I wonder as what are the points of difference between a Linear complex and a simple graph? Or are they both same?

Free programs to draw graphs?
allow me to draw graphs, lines, curves such as parabolas, set intervals with sliding bars etc.
I have tried geogebra but it is very limited and is a pain to use. For example, you cannot set a line to have a particular gradient, you can only draw a line and then measure the gradient afterward. And to plot parabolas, you cannot plot equations but rather do it in a microsoft paint style.

Trying to understand statistics/hypothesis testing. The example in the book discusses using a Z-Test. I am familiar with and on an intuitive level, I understand a Z-score, a Z-score basically measures how many standard deviations from the mean a point in a sample space is. This makes sense to me.
What I do not understand is why for a Z-test, we seemingly take the Z-score and divide it by $\sqrt{n}$ ?
Can anyone explain the difference, it seems like we are moving away from the intuitive explanation of "number of standard deviations from the mean" which is how we measure the probability via the area under the curve

How do you find the domain and range of $y=(x^2)-<!--\; -\; -->6x+1$?