Statistics Projects for High School Students

What factors determine the value of $$\mathrm{\alpha <!--\; \alpha \; -->}$$ for three distributions?

If x has a normal distribution with mean $$\mathrm{\mu <!--\; \mu \; -->}=15$$ and standard deviation $$\mathrm{\sigma <!--\; \sigma \; -->}=3$$, describe the distribution of $$\stackrel{¯<!--\; ¯\; -->}{x}$$ values for sample size n where n = 4, n = 16 and n = 100. How do the $$\stackrel{¯<!--\; ¯\; -->}{x}$$ distributions compare for the various sample sizes?

Undergraduate summer activities in the US or Europe?
I a currently a college freshman and I would like to do something math-related in the summer. I will have taken all of the basic courses except for analysis and set theory by the end of the summer (calculus,linear algebra, modern algebra, topology). I would like to know if there is anything out there for me, preferably something to which applications have not yet closed.
I think there are both summer schools and research summers or something like that. I have never done any research before though (not even close). And I doubt I could be able to without a lot of help.
So mainly I would like to know about the current panorama for math summer opportunities. I would also like to know if a dedicated student would be able to profit from a research summer. And finally if it would be plausible for a freshman to be accepted (I'm from Mexico if it helps).

What is a good book to learn all of precalculus?
I need a no-fluff book with great exposition on precalculus. It should cover up intermediate algebra, trigonometry and anything else needed to get a strong preparation for Spivak's Calculus. It shouldn't contain annoying images or anything agitating, just serious math. But above all things, it should be very comprehensive and rigorous. It should help me to understand the concepts, and not just memorize them like we're supposed to do with most American textbooks...

Are the actuarial exams hard? I heard that they're hard. is this proper? Are they like the qualifying checks in grad college? as an example, is the opportunity exam and the monetary math examination comparable to qualifying assessments (e.g. desires months and months of have a look at)?

For each of the binomial distributions, compute the mean, variance, and standard deviation. n=600, p=0.52

Which of the following is not true regarding the normal probability distribution? (asymptotic, family of distributions, only two outcomes, 50 percent of the observations greater than the mean)

Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial. Under what conditions is it appropriate to use a normal approximation to the binomial?

I'm not sure if the idea I have about them is right or wrong.
My professor defines four possible actions a Turing machine can do on a given input string:
Hang: The turing machine goes off the left end of the tape and "hangs"
Loop: The turing machine goes in a loop- never halts
Accepts: Turing machine halts in an accepting state
Rejects: Turing machine halts in a rejecting state
Is a turing recognizable language simply one that may either hold or loop? How do I determine if it could cling or loop? simply run it thru the system and if it does not halt on the rejecting state (or accepting) and its not part of the language of the TM then I determine its not decidable- so it must be recognizable? and then the decider is that if the language is assured to just accept or reject? What about languages that aren't recognizable? What might they do? as it seems that every one languages would be recognizable until it would be viable for the language to now not be inside the language of the turing system- but it halts inside the accepting kingdom anyways. Which looks like it would be because of bad layout of the turing system as opposed to the language itself.

Model theory is typically based on a formal language whose production rules and syntax are designed to formalize the deductive process, and as such typically include predicate or relation symbols. Obviously, any predicate by itself constitues a (atomic) formula, but any formula, when interpreted in a model, corresponds to a predicate as well, insofar as the formula corresponds to a definable subset of the model's universe which one could then define as the interpretation of a predicate symbol.
Neither of those correspondences are bijections, however though evidently predicates are extraneous, so the question is - are they blanketed in the language for the identical cause that the established quantifier is included no matter being able to be described using handiest the existential quantifier and negation image, i.e. for comfort? Or is the inclusion of predicate symbols genuinely important, either in version concept particularly or in the philosophical motivation as a rigorous examine of the deductive procedure?

I would love to study a math plotting software which could be helpful in visualizing subjects in advanced calculus (my on the spot want). it might additionally be useful if the mathematics plotting software turned into of a few use in electric engineering, however this is not mandatory. the choice standards is listed right here in lowering weight:
Ease of Use (syntax and techniques that are intuitive and easy to adapt to other problem areas)
Healthy ecosystem (lots of tutorials, examples online, books and other resources
Industry use (looking for the most commonly used software suites within engineering and science)
Adaptability (commonly used outside mathematics. ie. electrical engineering, modeling).
I have narrowed my search down to:
Matlab
Mathematica
Maple
But this list is by no means exclusive. Currently I am leaning towards Matlab, because I have seen it being used in upper year courses in my electrical engineering program.
I would appreciate your input with regard to which software suite would be best and why. Thank you.

The answers to the questions have distributions with different amounts of variability. Would you expect these questions to produce distributions with a lot of variability or very little variability? a. How tall are high school students? b. What are the scores on a hard math test? c. How much actual medicine is in each pill?

What is the difference between ANOVA and ANCOVA?
In the context of using only experiment data for ANOVA analysis, ANCOVA offers post hoc statistical control. Is this a valid conclusion and why?

Identify the distribution (normal, Student t, chi-square) that should be used in each of the fo llowing situations. If none of the three distributions can be used, what other method could be used? In constructing a confidence interval estimate of p, you have 1200 survey respondents and 5% of them answered "yes" to the first question.

I'am finishing my undergraduate degree in pc technological know-how and in spite of having needed to take a few math training my math capacity is still quite terrible. I struggled plenty with it which I consider changed into due to missing a few portions of know-how that I had to realize and not seeing the large photograph. Now i'am reading neural networks and seems they require pretty some math(eg: the backpropagation set of rules uses the chain rule). some human beings say you do not need the maths but I don't think I will be capable of to understand neural networks absolutely with out it. or even if I could get away with i would in all likelihood nevertheless want the mathematics later on.
i have approximately a month that i'm able to dedicate completely to this quest and i am determined to examine linear algebra and multivariate calculus on this time frame. i can start with linear algebra (doesn't depend on calculus, proper?) they have got solutions so I ought to be able to easily tune my progress. I also observed this path from Berkeley Math a hundred and ten. Linear Algebra. It would not have video lectures but it has greater assignments with answers so i'm able to exercise even greater. As for textbooks MIT uses "advent to Linear Algebra, Fourth version, Gilbert Strang" and Berkeley uses "Linear Algebra through S.H. Friedberg,A.L. Insel and L.E. Spence,Fourth edition". people here appear to mention true matters approximately them.
I'am beginning this journey the following day. in the suggest time i'd want to get some advice. Do you've got any recommendation with the intention to make this method smoother? Are there every other assets I should recognize approximately?

The normal distribution is a good estimate for which of the binomial distributions. n=50, p=0.7

How many normal distributions are there? (1, 10, 30, 1,000, or infinite-pick one)

The normal distribution is a good estimate for which of the binomial distributions. n=200, p=0.08

What relationship exists between the standard normal distribution and the box-plot methodology for describing distributions of data by means of quartiles? The answer depends on the true underlying probability distribution of the data. Assume for the remainder of this exercise that the distribution is normal. Can you now better understand why the inner and outer fences of a box plot are used to detect outliers in a distribution? Explain.

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If two normal distributions have the same mean and standard deviation, then they have the same shape.