# Tagged Questions

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### Finding probability given mean and standard deviation

I don't know how to approach this problem: X is normally distributed with a mean of 200 and a standard deviation of 10. Find P(X ≥ 203)
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### Basic Statistics find variance and standard deviation [closed]

Baseball Team Batting Averages Team batting averages for major league baseball in 2005 are represented below. Find the variance and standard deviation for each league. Compare the results. NL ...
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### Beginner Econometrics question about probabilities for a normal variable

$Y \sim N(\mu, \sigma^2)\implies (Y-\mu)/\sigma$ Prove that this has a Mean of $0$ and a Variance of $1$.
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### When plotting a bell curve from an array of values, is it possible that +/- 2 standard deviations from the mean can fall outside the range of values?

First, this is not homework, it is actually for work. It's been a couple of years since I've done stats and need some help! I've googled for this problem but was unavailable to find any resources that ...
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### Finding the 99% of a normally distributed graph

The heights of adults are normally distributed with a mean of 187.5 cm and a standard deviation of 9.5 cm. A standard doorway is designed so that 99% of adults have a space of at least 17 cm over ...
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### Statistics - Calculating Mean given standard deviation and percentage.

This is one of our homework problems for Statistics. I'm really stuck on this one, and it would be great if someone could show me how to solve this, or at least set up the equation. The weights of ...
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### Unbiased sample standard deviation of a custom/unknown probability distribution

Hi i must determine the unbiased sample standard deviation of an unknown probability distribution.I dont have the data of the full population so i must work with a sample. Now according to Wikipedia ...
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### How to estimate the standard deviation in this normal distribution?

There is this simple looking basic statistics question that asks to estimate its mean and standard deviation. I have some doubts and just want to make sure whether my working is correct. For part ...
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### Standard deviation in normal distribution

A manufacturer uses a machine to make metal rods.The diameter of the rods follow a normal distribution with a mean of 1cm and a standard deviation of 0.02cm If the standard deviation of the diameters ...
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### Finding the percentile of a value given other percentiles

I am using someone else's research and only have part of the data. I want to find the percentile of a value, such as 350.2, based upon the data given. The following is known: mean = 308.2 The ...
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### Showing deviation of data on a fixed scale

I'm creating a chart in D3 which shows the Mode from a large (1mil +) dataset; and colors it according to the standard deviation of the dataset. But the issue is that I need to map the range (Red ...
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### Measure dispersion of a set of values resides in a range

I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ...
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### Adding stochastic variables random variables where one has time component

Based on GLS regression I have identified two random variables lets call them A & B ...
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### Population confidence interval from sample SD and sample mean?

A sample has: $$\text{a sample size } n = 70,$$ $$\text{sample standard deviation } s = 184.43,$$ $$\text{and a sample mean } \bar{x} = 564.15.$$ Compute a 95% confidence interval for the population ...
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### Is the variation of the mean 0, and the variance of standard deviation just the variance?

Just trying to get some properties straight. Was looking at a problem online which reads: Let X be a random variable with mean μ and variance σ2. What is the variance of X/σ+10μ? The solution of ...
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### Clarification on z-score

I have been reading a Statistics book and they show the following formula for z-score: $z = \frac{x - \mu}{\sigma}$ And then they explain about the $\mu$ and the $\sigma$ in the formula like this: ...
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### Find StdDev of a percentage list

I need to find Standard Deviation of a percentage list, e.g. [0.5, 0.8, 0.8] in Python would give: ...
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### SD from Mean and Median

Given the mean and median of a dataset, is it possible to compute the standard deviation of the dataset?
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### Value of n to ensure the mean is within a 95% confidence interval

A random sample of size n is obtained from normal distribution. Calculate how large n must be to ensure that the sample mean lies within 0.25s.d of the mean with probability of 95%. I know the ...
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### Standard deviation with multiple means and deviations

The amounts of a certain mineral that can be produced in a day from mines $1$, $2$, and $3$ are independent normal random variables with means equal to $80$, $90$, and $75$ pounds, respectively, ...
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### Exponential deviation with two $x$ values

I recently got interested in this topic of standard deviation. My TA did not have any time to go over this topic so I was trying to teach myself it recently. My TA said if he had more time he would ...
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### Margin of error for quotient of two measurements

I need to find the total margin of error for calculating velocity, while I have margins of error for time and distance. Actually the margins are the same (as both measurements were based on GPS - but ...
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### Standard deviation shouldn't reduce?

I need to do a algorithm to calculate an integral via Monte Carlo Method, and for a purpose of simulation, I need to calculate the standard deviation of a sample generated in my program. My problem is ...
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### A Sample with two Standard Deviation

Question : In a batch chemical process, two catalysts are being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1 and a ...
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### Uncertainty on an estimator

Well first I want to say that I have a very weak background in stats/probability but I still hope that the question I want to share with you makes sense. I have a set of binary (coming from a set of ...
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### I need help with this review question. Business Calculus/Statistics

The question is: The scores on a test have a mean of 100 and a standard deviation of 8. A personnel manager wishes to select the top 60% of applicants. Find the cutoff score. Assume the variable is ...
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### Variences and adding them from independent random variables?

If I have 3 random varibles X, Y and Z and X=Y+Z then var(X)=var(Y)+var(Z), but Y=X-Z therefore var(Y)=var(X)+var(Z), it is clear that these two contridict, so what makes one of them right and the ...
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### How to weight three different variables to create a ranking

I have data on the graduation rate, tuition, and average student income (a measure of accessibility) for about 7,000 colleges and universities in the U.S., and I'm trying to compose an interactive in ...
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### Estimate standard deviation of sample

You have a random sample of 25 objects with mean weight of 24 grams, estimate the standard deviation of the sample. In addition, you know it's supposed to be 25 grams with a deviation of 1 gram, but ...
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### Taking the standard deviation over multiple assignments?

Lets say that a group of students all take 5 tests, with the average and standard deviations as follows: test 1: mean 43/50, SD 8 test 2: mean 23/30, SD 4 test 3: mean 56/70, SD 12 test 4: mean ...
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### Probability and Standard Deviation

Hey I'm confused about how to do this kind of problem. I can't figure out how to find the standard deviation. There are on average 4 tetanus cases reported in the US each month. What is the ...
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### how to find standard deviation when given a percentage?

I'm stuck on this question, can anyone help? An electronics company's biggest seller is a talking toy. Of the toys produced, 4% have a defective voicebox. A quality control tech randomly collects 250 ...
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### stdev and mean from gaussian fit vs. from classical formula

I have a set of data - measured speed of molecules in water. I made a histogram and fitted it with function $$A\exp\frac{(x-B)^2}{C}$$ calculating mean and standard deviation from values B and C If I ...
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### Confidence intervals and dividing by $n^{0.5}$

I am studying a-level and am confused when I divide the standard deviation by $n^{0.5}$ when doing confidence intervals. To put it another way when I don't divide by it? (where $n$ is the number of ...
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### Identification of linear regression function under $\ell_1$-norm criterion.

Consider a linear system \begin{align*} y = \theta^Tx + e, \end{align*} where $x\in\mathbb{R}^n$ and $e\in\mathbb{R}$ are independent Gaussian random variables with distribution $\mathcal{N}(0,I_n)$ ...
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### Standard Deviation and Mean

take a look at this question: The sample from Population A has a mean of 35 and a standard deviation of 1. The sample from Population B has a mean of 45 and a standard deviation of 15. Which of ...
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### Confidence interval for n=1, unknown standard deviation

Is there any way to calculate a confidence interval (or otherwise gauge the reliability of a sample) when you have a sample size of one and you don't know the population standard deviation? I work at ...
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### What is the corrected sample standard deviation when there is only one sample?

What do we say about the corrected sample standard deviation when the sample size is one? Do we just assume it is 0? Is it even meaningful? The usual equation seems to fall apart here because N - 1 ...
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### Establishing the upper and lower bounds of normal using standard deviation

I understand the concept of standard deviations and z-values, but I'm trying to figure out if standard deviations alone are good for establishing the upper and lower bounds for normal. For example, if ...
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### Percentage with only standard deviation and mean given. [closed]

I have some questions that I really need help with. The mean mark for an IQ test in the population is 100, with a standard deviation of 16.5. The IQ is normally distributed. Your IQ is 113. a. ...
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### Probabilities and Estimation of average and standard deviation

I've done a good bit of this number but I have trouble with part 2. I'll show you my work and the questions I can't figure in bold. A guy has a machine that scans his apples. The machine rules are : ...
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### Fast way to recalculate average and standard deviation as new values arrive

Say I have a stream of values arriving all the time, and I want to get the average and standard deviation of only the last $n$ values. If I already have the average $V$ for values $v_1, ..., v_n$, ...
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### hypothesis testing two sample problem and standard error of mean

In my homework, I was asked to find the standard error of mean for 2 cases and then do the 5% and 1% test for both of them. I know how to work out stand error of mean, but I don't know how to use it ...
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### X and Y are two random variables, what is the standard deviation of X - 2Y

I have: E(X) = 10 E(Y) = 12 Var(X) = 4 Var(Y) = 9 covariance = 2 I know that for: ...
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### Relationship between median and standard deviation

I have some data and I added Gaussian noise with zero mean ($\mu=0$) and standard deviation ($SD=SD$). I was interested to see the behaviour of the noise to the data after integrations. I integrated ...
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### Why does variance divide by $n-1$? [duplicate]

The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ I read that $n-1$ is used instead of just $n$ when we are measuring the variance of a sample taken from a bigger population. I don't ...
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### Why is variance squared?

The mean absolute deviation is: $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$ The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ So the mean deviation and the variance are ...
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### question about Mean absolute deviation formula

$$\frac{\sum_{i=1}^{n}(x_i-\bar x)}{n}$$ This method will not work for calculating the mean deviation. Instead we have: $$\frac{\sum_{i=1}^{n}|x_i-\bar x|}{n}.$$ I'm not quite understanding why ...