Stepwise Descriptive Statistics Learning

Use this type of statistics to analyze data when you have more than one dependent variable.
Use one of the following key terms to answer each of the following questions.

KEY TERM BANK (separated by commas):
Univariate, Multivariate, meta-analysis, F-ratio, interaction, main effect

13 % of people took a math course. What is the probability that in a 350 randomly selected sample, less than 40 people take the course?

So I have $X\sim <!--\; \sim \; -->Bin(350,\frac{13}{100})$
Then let $Y\sim <!--\; \sim \; -->N(\frac{13}{100},{\sqrt{0.00032314}}^2)$
I want $P(X<40)=P(\stackrel{^<!--\; ^\; -->}{p}<\frac{4}{10})$
Then $P(z<\frac{\frac{4}{10}-<!--\; -\; -->\frac{13}{100}}{{\sqrt{0.00032314}}^2})$ which is obviously very wrong.
Where did it go wrong, and why did it go wrong?

How do you write a rule to represent the relationship between the number of typed words and the time in which they are typed if a typist types 45 words per minute?

In order to campare the difference between clinical diagnosis and B ultrasonic for 120 gallstones patients. Each patient with two kind of Methods for the diagnosis, the results as following: The positive rate of clinical diagnosis is 50%, The positive rate of B ultrasonic is 60%, The positive rate of two methods at the same time is 35%. How to analysis the difference between two methods?

What is the range of the function $F(X)=(X-<!--\; -\; -->1{)}^2+6$?

chromatic number of a graph versus its complement
What can be said about the rate of growth of f(n), defined by
$f(n)=\underset{|V(G)|=n}{min}[\mathrm{\chi <!--\; \chi \; -->}(G)+\mathrm{\chi <!--\; \chi \; -->}(\stackrel{¯<!--\; ¯\; -->}{G})],$
where the minimum is taken over all graphs G on n vertices.
Two observations.
(1) Either G or $\stackrel{¯<!--\; ¯\; -->}{G}$ contains a clique on roughly logn vertices by Ramsey theory, so $f(n)\ge <!--\; \ge \; -->c_1\log <!--\; \; -->n$ for some constant $c_1>0$.
(2) If G=G(n,1/2) is a random graph, then $\mathrm{\chi <!--\; \chi \; -->}(G)\approx <!--\; \approx \; -->\mathrm{\chi <!--\; \chi \; -->}(\stackrel{¯<!--\; ¯\; -->}{G})\approx <!--\; \approx \; -->n/\log <!--\; \; -->n$ n/ log n almost surely, so we also have $f(n)\le <!--\; \le \; -->c_{2}n/\log <!--\; \; -->n$ n/log n for some constant $c_2>0$.
These bounds seem hopelessly far apart.
Can we improve on the bounds
$c_1\log <!--\; \; -->n\le <!--\; \le \; -->f(n)\le <!--\; \le \; -->c_{2}n/\log <!--\; \; -->n$
for all sufficiently large n?

How does the shielding effect affect atomic radius?

Prove that a self-complementary graph has radius 2 and diameter 2 or 3.
I think that is one of the well-known properties of self-complementary graphs, but I am having some troubles trying to prove it. The facts that, if $G\cong <!--\; \cong \; -->\stackrel{¯<!--\; ¯\; -->}{G}$, then both graphs G and $\stackrel{¯<!--\; ¯\; -->}{G}$are connected, and that, for any graph, if $rad(G)\ge <!--\; \ge \; -->3$ then $rad(\stackrel{¯<!--\; ¯\; -->}{G})\le <!--\; \le \; -->2$, and that if $diam(G)\ge <!--\; \ge \; -->3$ then $diam(\stackrel{¯<!--\; ¯\; -->}{G})\le <!--\; \le \; -->3$, should make the proof quite easier, but I don't know how to develop it. Could you help me? Thanks in advance!

I am attempting to find an unknown value given the probability of the range of X. I am unsure of how to calculate the value given the added constants defined in the problem and which values I need to use to look up the z-scores to plug into the x = z + $\mathrm{\mu <!--\; \mu \; -->}(\mathrm{\sigma <!--\; \sigma \; -->})$. I have found z given probability of 0.95 to be 1.644853. Not really sure if that is the correct value to use or how to go from here? Here is the problem:
A random variable X has the distribution $N(1500,(200{)}^2)$. Find B, where $P(1500-<!--\; -\; -->B<X<1500+B)=0.95$

When you look up the probability in a z-table is that the value less than or less than or equal?
For example is it $p(z<2.35)=.0094$ or is it $p(z\le <!--\; \le \; -->2.35)=.0094$?
And if they aren't equal then how would you calculate the other one?
I would think given any single point has 0 width that it shouldn't matter, but I am not sure.

What is the z-score of sample X, if

How do you find the domain and range of $\sqrt{x-<!--\; -\; -->8}$?

Transforming an entire distribution of scores into z-scores changes an originally positively skewed distribution to a negatively skewed z-score distribution. True or False

When is meta-analysis is most useful?

complete k-partite graphs
I am trying to solve the following problem:
Let G be a nonempty graph with the property that whenever $uv\notin <!--\; \notin \; -->E(G)$ and $vw\notin <!--\; \notin \; -->E(G)$, then $uw\notin <!--\; \notin \; -->E(G)$. Prove that G has this property if and only if G is a complete k-partite graph for some $k\ge <!--\; \ge \; -->2$. (Consider $\stackrel{¯<!--\; ¯\; -->}{G}$).
The converse is straightforward and is given by the definition of the complete k-partite graphs, however, the direct way is not trivial and I could not get it.

A survey found that​ women's heights are normally distributed with mean 63.4
in and standard deviation 2.4
in. A branch of the military requires​ women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too​ tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest​ 1% and the tallest​ 2%, what are the new height​ requirements?
a) The percentage of women who meet the height requirement is:
The website says I am supposed to use $\frac{z-<!--\; -\; -->\mathrm{\lambda <!--\; \lambda \; -->}}{2.4}$
doing so gives me $\frac{16.6}{2.4}=7.086$ This value literally is useless. What am I doing wrong?

Underline the correct word (in the parenthesis) to complete the sentence.
4) When normal scores are transformed into z-scores, the resulting z-scores will have a mean of (0, 1 ).
5) For a normal random variable, the probability of observing a value less than or equal to its mean is (0,0.5, 1).

What is the z-score of X, if n = 25, ${\displaystyle \mu =60}$, SD = 12, and X =58?

assuming that the system downtime is normally distributed with mean ($\mathrm{\mu <!--\; \mu \; -->}$)4.47 sec and standard deviation($\mathrm{\sigma <!--\; \sigma \; -->}$) of 0.38 sec.
By using the cumulative (to the left) Z score table,
a) find the probability that the system downtime is more than 5 sec.
z score = (n-$\mathrm{\mu <!--\; \mu \; -->}$)/ $\mathrm{\sigma <!--\; \sigma \; -->}$
= (5-4.47)/0.38
= 1.39
the probability for 1.39 in the z score table is 0.9177
so, P(x$\le <!--\; \le \; -->$5)= 0.9177
P(x>5)= 1- 0.9177
= 0.0823
b) what is the minimum downtime duration for the worse 5% ?
(i already got the answer for a, i just don't quite understand the meaning of 'for the worse 5%' )

What type(s) of distributions can a z-test be applied to?