I'm new to studying z-scores and I've been told that for a gaussian statistic, around 95% of the val

Callum Dudley 2022-07-04 Answered
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,
μ 2 σ μ + 2 σ A e ( ( x μ ) / σ ) 2 d x = 0.95 + A e ( ( x μ ) / σ ) 2 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?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Caiden Barrett
Answered 2022-07-05 Author has 20 answers
Using a change of variables x = μ + σ t, and inserting the missing 1/2 in the exponentials, the left side can be evaluated using the error function
A 2 2 e t 2 / 2 d t = 2 π A erf ( 2 )
while the right side is 2 π A. In fact erf ( 2 ) 0.9544997360.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-08-12
If X is N ( μ ; σ 2 ), then show that Z = ( X μ ) σ is a standard normal random variable; that is, N ( 0 ; 1 )

Here is how far I have gotten:
P ( Z z ) = P ( X z σ + μ ) = x μ σ z e y 2 2 2 π d y .
I used x = y σ + μ as my change of variable.
1.) Is my result correct so far?
2.) And what is my next step? This integral is out of my scope.
asked 2022-08-22
I know that you can use a z-table to find p-values given a z-score, however I am curious if you can calculate it without the z-table or a calculator. Is it possible? If so, how do you do it? I've tried searching, but the only thing that came up was a post on the Actuarial Outpost, and none of the answers really addressed the question.
Note: I am curious because I want to write a Python program that will do this, and writing an entire z-table, and then searching the table for a given value seems incblackibly tedious and inefficient. I am aware that the scipy library can do this, however it seems kinda lazy, and on top of that I'm just curious.
edit: The answer was actually really simple, just take the integral of the normal distribution and approximating it. However, this doesn't seem satisfying or tangible enough for me, mostly because I can't convert it to code-form (sorry for the trouble by the way). Are there any other ways?
asked 2022-07-16
What is the z-score of X, if n = 204, μ = 15 , SD =1, and X =35?
asked 2022-07-16
What is the z-score of sample X, if n = 49 , μ = 75 , S t . D e v . = 42 , a n d   E X = 88
asked 2022-10-13
What is the purpose of calculating z-scores?
asked 2022-08-12
Fine the area , to the nearest thousandth, of the standard distribution between the given z-scores. Z equals 0 and z equals 1.5
asked 2022-06-25
I was given a question where I was supposed to find the probability of obtaining y between two scores, however when I input my answer it tells me that I'm wrong, the question is given below along with my answer to the question:

Question
For a normal distribution with sample mean =−19 and standard deviation =6.85 find p ( 16.15 y 15.27 ), where y is a random draw from the normal distribution. Round to 4 decimal places.

My answer
I obtained the z scores for both the y values −15.27 and −16.15 and their respective z scores are 0.5445 and 0.4161. The probability under the curve with a z score of 0.5445 is 0.7054 and the probability under the curve with a z score of 0.4161 is 0.6628. With those two probabilities, I obtained the difference (getting 0.0426) and I put in that answer and was told that I was wrong. Can someone give me insight as to what I'm doing wrong?

New questions

i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?
historical past/issues:
My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.
i have taught this magnificence three times earlier than. (a part of the purpose that i'm posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik's dice.
the students' math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren't. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed "pre-calculus": trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.
So, any ideas? preferably, i'd like to find some thing a bit "sexy" (like the Rubik's cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of "see" institution idea on the cube became pretty popular.
(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)