What is the z-score of sample X, if $n=9,\mu =56,SD=30,\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}E\left[X\right]=32$?

suchonosdy
2022-07-23
Answered

What is the z-score of sample X, if $n=9,\mu =56,SD=30,\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}E\left[X\right]=32$?

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minotaurafe

Answered 2022-07-24
Author has **22** answers

The z-score for a sample mean is

$z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{9}}}$

$\overline{x}=E\left[X\right]=32$

$\mu =56$

$\sigma =30$

$n=9$

Therefore,

$z=\frac{32-56}{\frac{30}{\sqrt{9}}}=-\frac{24}{10}=-2.4$

$z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{9}}}$

$\overline{x}=E\left[X\right]=32$

$\mu =56$

$\sigma =30$

$n=9$

Therefore,

$z=\frac{32-56}{\frac{30}{\sqrt{9}}}=-\frac{24}{10}=-2.4$

asked 2022-06-21

What books are there that cover elementary algebra, but are not bloated with pedagogically padding?. I searched in this website and the web in general, but the books I could find about elementary algebra are full of pedagogical padding (lots of meta, repetitive examples, fancy formatting, little-relevance images and so on, as if they were written for kids); I find that distracting, and it makes harder to locate material as the density is much lower than in a book like Serge Lang's Algebra or Rudin's Prinicples of Mathematical Analysis.

Could you please recommend a book that covers (even if it is not its main topic) elementary algebra, but from an approach closer to that found in undergraduate-level books (including proofs and excluding pedagogical padding)?.

I know most of what is included in an elementary algebra course, but I want to review this area to make sure I will not miss something elementary when studying more advanced mathematics. I mainly want to review the manipulations of real and complex expressions, rather than things like what a function or a linear equation is.

Could you please recommend a book that covers (even if it is not its main topic) elementary algebra, but from an approach closer to that found in undergraduate-level books (including proofs and excluding pedagogical padding)?.

I know most of what is included in an elementary algebra course, but I want to review this area to make sure I will not miss something elementary when studying more advanced mathematics. I mainly want to review the manipulations of real and complex expressions, rather than things like what a function or a linear equation is.

asked 2022-07-16

What is the z-score of X, if n = 204, $\mu =15$, SD =1, and X =35?

asked 2022-04-07

Let ${Y}_{1},{Y}_{2},...,{Y}_{n}$ be random samples from a normal distribution where the mean is 2 and the variance is 4. How large must n be in order that $P(1.9\le \overline{Y}\le 2.1)\ge 0.99$?

My attemp^

We are computing for the sample mean of our random sample that was given in the problem. By definition, $z=\frac{\overline{Y}-\mu}{\frac{\sigma}{\sqrt{n}}}$. So rewrite the equation so we can transform the data to make the mean 0 and the standard deviation 1. If I do that, I get,

$P(\frac{1.9-2}{\frac{2}{\sqrt{n}}}\le z\le \frac{2.1-2}{\frac{2}{\sqrt{n}}})\ge \mathrm{0.99.}$ This means that

$P(\frac{-0.1}{\frac{2}{\sqrt{n}}}\le z\le \frac{0.1}{\frac{2}{\sqrt{n}}})\ge \mathrm{0.99.}$ This also means that

$P(-0.05\sqrt{n}\le z\le 0.05\sqrt{n})\ge \mathrm{0.99.}$ I am not really sure what to do after this step. I am trying to use the definition of the normal distribution, however that was too difficult to do.

Do you guys know what to do after this step?

My attemp^

We are computing for the sample mean of our random sample that was given in the problem. By definition, $z=\frac{\overline{Y}-\mu}{\frac{\sigma}{\sqrt{n}}}$. So rewrite the equation so we can transform the data to make the mean 0 and the standard deviation 1. If I do that, I get,

$P(\frac{1.9-2}{\frac{2}{\sqrt{n}}}\le z\le \frac{2.1-2}{\frac{2}{\sqrt{n}}})\ge \mathrm{0.99.}$ This means that

$P(\frac{-0.1}{\frac{2}{\sqrt{n}}}\le z\le \frac{0.1}{\frac{2}{\sqrt{n}}})\ge \mathrm{0.99.}$ This also means that

$P(-0.05\sqrt{n}\le z\le 0.05\sqrt{n})\ge \mathrm{0.99.}$ I am not really sure what to do after this step. I am trying to use the definition of the normal distribution, however that was too difficult to do.

Do you guys know what to do after this step?

asked 2022-06-16

The proportion of people who like playing basketball is 2%, so a student randomly sample 1000, but find the proportion is 4%, if the true proportion is 2%. What the probability that this student detect at least 4% in random sample?

I used the formula, but found the z score is 4.51 which is impossible I think.

I used the formula, but found the z score is 4.51 which is impossible I think.

asked 2022-06-21

Given is a lognormal distribution with median $e$ and mode $\sqrt{e}$. What is the variance of the lognormal distribution?

Not sure how to solve this. A variable $Y$ has a lognormal distribution if $\mathrm{log}(Y)$ has a normal distribution. So I'm thinking you can solve the question by finding the mean and standard deviation of the associated normal distribution by using the given median and mode. But I don't know how to. For a normal distribution, the median and mode equal the mean, but for a lognormal distribution they evidently do not. How to use these values to find the variance?

Not sure how to solve this. A variable $Y$ has a lognormal distribution if $\mathrm{log}(Y)$ has a normal distribution. So I'm thinking you can solve the question by finding the mean and standard deviation of the associated normal distribution by using the given median and mode. But I don't know how to. For a normal distribution, the median and mode equal the mean, but for a lognormal distribution they evidently do not. How to use these values to find the variance?

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What is the z-score of sample X, if $$

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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 $G\cong \overline{G}$, then both graphs G and $\overline{G}$are connected, and that, for any graph, if $rad(G)\ge 3$ then $rad(\overline{G})\le 2$, and that if $diam(G)\ge 3$ then $diam(\overline{G})\le 3$, should make the proof quite easier, but I don't know how to develop it. Could you help me? Thanks in advance!