Interpreting Z Scores Made Easy with Our Experts Help

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,
$\int_{μ - 2 σ}^{μ + 2 σ} A e^{- ((x - μ) / σ)^{2}} d x = 0.95 * \int_{- \infty}^{+ \infty} A e^{- ((x - μ) / σ)^{2}} d x$
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?

prirodnogbk 2022-07-02

I have been reading a Statistics book and they show the following formula for z-score:
$z = \frac{x - μ}{σ}$
And then they explain about the $μ$ and the $σ$ in the formula like this:

These are the mean and standard deviation of data containing the value x.

But is that so ? I don't think the mean and standard deviation should contain the value x.

Sovardipk 2022-07-01

On the first periodic exam in Statistics, the population mean was 70 and the population standard deviation was 9. How to determine the standard score of a student who got a score of 88 assuming that the scores are normally distribtued?

Pattab 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?

kokoszzm 2022-07-01

I am comparing 2 variables and have an outlier in x of 82.27. I want to find the z score of this outlier. When using the z score equation x-mean/standard deviation, do I use the mean and standard deviation of my x values or y values?

Maddy Sheehan2022-06-26

Based on historical data, your manager believes that 35% of the company's orders come from first-time customers. A random sample of 103 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.22 and 0.4?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer = (Enter your answer as a number accurate to 4 decimal places.)

Yesenia Sherman 2022-06-25

I have learned that z-scores are "Measures of Relative Standing" and that they can be used to compare two scores that are from different normal distributions.

For example if I wanted to compare how I performed

with a 85% in a math class with mean 70 and std dev 15;
and
with a 70% in a english class with mean 50 and std dev 15;

I would use the z-score formula to calculate a relative value for two situation and use it to compare them.

However why is it not enough just to compare each classes with the mean and use this as a basis for comparison? For example

85% -70% = 15%
70% - 50% = 20%
20 > 15 therefore I must have performed better in english

I know this is incorrect but I don't understand why. thx for the help

Arraryeldergox2 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 $p (- 16.15 \leq y \leq - 15.27)$ , 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?

flightwingsd2 2022-06-24

Having some issue with the concept of Z score.
When exactly do I use $Z = \frac{\bar{X} - u}{σ}$
and when do I use $Z = \frac{\bar{X} - u}{\frac{σ}{\sqrt{n}}}$
I get very confused with in what situation should be using which Z calculation. Really appreciate it to have someone explain the concept

George Bray 2022-06-24

What is the formula to convert a z-score to its appropriate percentile? I assume there is a formula.

arridsd9 2022-06-21

Can anyone explain when should I add 0.5 to the z-score?

Cherry Satingasin2022-06-19

In hypothesis testing, we have scenarios that have both dependent and
independent samples. Give an example of an experiment with (1)
dependent samples and (2) independent samples.

Gybrisysmemiau7 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.

excluderho 2022-06-12

A distribution has a standard deviation of o=10. Find the z-score for each of the following locations in the distribution.
a) Above the mean by 5 points b) Above the mean by 2 points c) Below the mean by 20 points d) Below the mean by 15 points
Please don't give me the answer, but explain how I would work this out.

Mohamed Abdurashid2022-06-03

Ten randomly selected people were asked how long they slept at night. The mean time
was 7.1 hours, and the standard deviation was 0.78 hour. Find the 95% confidence
interval of the mean time. Assume the variable is normally distributed.

Reginald Hanna 2022-06-03

I saw this somewhere. Is this right?
$P (z < - 4.3333) = 0.00003$
Most z-score table stops at 3.4. If this is right, kindly explain how it was gotten. Thanks

Eliaszowyr1 2022-05-27

From a given z-score, what is the formula for calculating the probability of the deviation being due to chance?
e.g.
Given z = 1.2 standard deviations
The chance probability p = 0.11507
How did we derive p? (i.e. the formula, without having to refer to the normal distribution table)

hard12bb30crg 2022-05-15

$X \sim N (15, 4)$
Find P( X > 18.7 | X > 11.7 ).
Attempt: Rewrite as P ( x > 18.7) - P( x > 11.7)
Using the phi function
$ϕ (1.85) - ϕ (- 1.65) = (0.9678) - (0.0495) = 0.9183$
Where did I go wrong?

Spencer Lutz 2022-05-13

I'm new here and was hoping you guys could help me with a statistics problem that I don't quite understand. I'm not sure if it's proper etiquette to ask for help on a specific homework problem here, so I apologize if this question is out of line.

Here is the problem:
Suppose a variable of a population has mean 5 and standard deviation 11. For samples of size 121, find $c$ so that $P (X > 2 c) = 0.3300$ .

Merati4tmjn 2022-05-09

I have a set of 1000 data points. I would like to estimate their mean using a confidence interval. I read somewhere that if the sample size, $n$ , is bigger than 30 you should use a t-score, and else use a z-score.
Is that true?

If you are working with statistics and probability, you might have used the Z scores calculator to determine the market volatility. If you take a look at the questions that have been provided below, you will notice that the Altman Z-score is also used to determine the relationship when you work with a group of scores. Make sure to check your sample data twice! The other answers or Z scores examples will help you to build the graphs and tell you not only about your value but how to distribute it and apply equations and the balance as you calculate.

Descriptive Statistics

Understanding Z Scores with Practical Examples