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

Kade Reese
2022-07-20
Answered

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

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Quenchingof

Answered 2022-07-21
Author has **14** answers

$=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$=\frac{43-23}{\frac{110}{\sqrt{121}}}=2$

$=\frac{43-23}{\frac{110}{\sqrt{121}}}=2$

asked 2022-07-07

Given the mean, median and mode of a function and have to find the probability density function.

mean: $\gamma -\beta {\mathrm{\Gamma}}_{1}$

median: $\gamma -\beta (ln2{)}^{1/\delta}$

mode: $\gamma -\beta (1-1/\delta {)}^{1/\delta}$

Also given that

${\mathrm{\Gamma}}_{k}=\mathrm{\Gamma}(1+k/\delta )$

$\mathrm{\Gamma}(z)={\int}_{0}^{\mathrm{\infty}}{t}^{z-1}dt$

$-\mathrm{\infty}<x<\gamma ,\beta >0,\gamma >0$

Now I understand how to calculate the mean, mode and median when given a probability density function. However I'm struggling to go backwards. I initially tried to "reverse" the process by differentiating the mean or median however I know this is skipping the substitution over the given limit.

I then looked for patterns with known distributions and realised they are from Weibull distribution however $\gamma -$. Does this mean essentially this is a typical Weibull distribution however shifted by $\gamma $ and therefore the pdf will be $\gamma -Weibullpdf"$

mean: $\gamma -\beta {\mathrm{\Gamma}}_{1}$

median: $\gamma -\beta (ln2{)}^{1/\delta}$

mode: $\gamma -\beta (1-1/\delta {)}^{1/\delta}$

Also given that

${\mathrm{\Gamma}}_{k}=\mathrm{\Gamma}(1+k/\delta )$

$\mathrm{\Gamma}(z)={\int}_{0}^{\mathrm{\infty}}{t}^{z-1}dt$

$-\mathrm{\infty}<x<\gamma ,\beta >0,\gamma >0$

Now I understand how to calculate the mean, mode and median when given a probability density function. However I'm struggling to go backwards. I initially tried to "reverse" the process by differentiating the mean or median however I know this is skipping the substitution over the given limit.

I then looked for patterns with known distributions and realised they are from Weibull distribution however $\gamma -$. Does this mean essentially this is a typical Weibull distribution however shifted by $\gamma $ and therefore the pdf will be $\gamma -Weibullpdf"$

asked 2022-07-04

I'm new to studying z-scores and I've been told that for a gaussian statistic, around 95% of the values lie within the area two standard deviations above and below the mean, which (in accordance to my interpretation) would imply,

${\int}_{\mu -2\sigma}^{\mu +2\sigma}A{e}^{-((x-\mu )/\sigma {)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=0.95\ast {\int}_{-\mathrm{\infty}}^{+\mathrm{\infty}}A{e}^{-((x-\mu )/\sigma {)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x$

Firstly, am I correct in my presumption? and secondly, is there any way to calculate the integral on the left to prove this point mathematically?

${\int}_{\mu -2\sigma}^{\mu +2\sigma}A{e}^{-((x-\mu )/\sigma {)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=0.95\ast {\int}_{-\mathrm{\infty}}^{+\mathrm{\infty}}A{e}^{-((x-\mu )/\sigma {)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x$

Firstly, am I correct in my presumption? and secondly, is there any way to calculate the integral on the left to prove this point mathematically?

asked 2022-07-16

I came here since I know this is the best place to ask a question.

I'm a first year student who changed his major to applied mathematics. In middle school I was a garbage math student, but I realized the importance of math in high school when I was introduced to amazing teachers who truly loved what they did. I put myself in tougher classes and eventually got to AP calculus. There was an error in my idea, I never really got a deep understanding of the stuff I was doing and was struggling since I didn't understand the basics and never really did practice problems.

This year I began to start over from scratch from pre-algebra working to pre-calculus. Even though I have already took Calculus.

I'm in a introduction to research class this semester and we are preforming a meta-analysis of some random topic and then presenting at the end of the semester. I'm really enjoying it, and I will definitely apply for more research as I progress through my undergraduate career. (Urge to Compute)

I know I'll probably never win a field's medal, but I'm really intimidated and humbled by the near perfect SAT math scores and Math Olympiad participants.

It's too late for me to have that, but the best quality I have is sticking with the concepts and problems until I can explain them to my dog. (Basically until I understand it)

I'm really sorry for the long post / soft question, I've just been thinking about this since 11th grade but never asked anyone about it.

Basically I'm just wondering if I'm wasting my time, and if there have been mathematicians that were in a similar situation. (Famous or not.)

Again, sorry for the soft question and thank you for taking the time to read this!

I'm a first year student who changed his major to applied mathematics. In middle school I was a garbage math student, but I realized the importance of math in high school when I was introduced to amazing teachers who truly loved what they did. I put myself in tougher classes and eventually got to AP calculus. There was an error in my idea, I never really got a deep understanding of the stuff I was doing and was struggling since I didn't understand the basics and never really did practice problems.

This year I began to start over from scratch from pre-algebra working to pre-calculus. Even though I have already took Calculus.

I'm in a introduction to research class this semester and we are preforming a meta-analysis of some random topic and then presenting at the end of the semester. I'm really enjoying it, and I will definitely apply for more research as I progress through my undergraduate career. (Urge to Compute)

I know I'll probably never win a field's medal, but I'm really intimidated and humbled by the near perfect SAT math scores and Math Olympiad participants.

It's too late for me to have that, but the best quality I have is sticking with the concepts and problems until I can explain them to my dog. (Basically until I understand it)

I'm really sorry for the long post / soft question, I've just been thinking about this since 11th grade but never asked anyone about it.

Basically I'm just wondering if I'm wasting my time, and if there have been mathematicians that were in a similar situation. (Famous or not.)

Again, sorry for the soft question and thank you for taking the time to read this!

asked 2022-06-21

The distribution is left-skewed if meanThe distribution is right-skewed if mean>median>mode.

Can mode lie between mean and median?

Can mode lie between mean and median?

asked 2022-07-16

What is the z-score of sample X, if $n=36,\text{}\mu =5,\text{}\text{St.Dev}=9,\text{}{\mu}_{X}=6$?

asked 2022-07-01

I need to figure out how to find what proportion of scores fall above a z score of 1.65. I'm having trouble and this hasn't been explained much in class. We have to use a z-table to get the correct scores so I'll supply them here.

In column b (area between mean and the z) the score is 0.4505 for a z score of 1.65. And in column c the score is .0495 for a z score of 1.65. I hope you guys can help me.

How do I figure out what proportion fall above 1.65?

In column b (area between mean and the z) the score is 0.4505 for a z score of 1.65. And in column c the score is .0495 for a z score of 1.65. I hope you guys can help me.

How do I figure out what proportion fall above 1.65?

asked 2022-06-10

Find the mode, we need to find the value of $x$ for which ${f}^{\prime}(x)=0$ and ${f}^{\u2033}(x)<0$. After applying derivative to the pdf, how do we proceed?