# normal

1. ### Distributions and means - confidence interval question

Hi folks, :wave: I think I did my research but I would like to be sure before continuing. My task is to find the mean price of a given item in a given country and I need to know how accurate my sample mean is vs. the actual population mean. Here is what I have. (My proposed, probably...
2. ### Calculating probability given mean and standard deviation

Hi I have looked around for this post on the forum but could not find one and have spent a while attempting this question: Given that X is normally distributed with mean 100 and standard deviation 9 and given a sample size of 16, compute the following: 1) mean and variance of X-dash 2)...
3. ### Xn~Exponential(.5) -> Xn~Normal. Use Chebychev's inequality

Xn are iid Exponential(.5). After using the central limit theorem, Xn is Normally distributed. Use chebychev's inequality to find out how large n be so that P(|Xn-2| < .01) > .95. I tried working on it and got the E(Xn) = 2n and Var(Xn) = 4n, and P(|Xn-2n| > .01) < (4n/(.01)^2)(1/n)= 40000...
4. ### I really need help on my homework!

Theres 2 questions I'm really stuck on. One has three parts and is of course one of those "you can't do the next step until you get the first step" kind of thing.\ 1.A set of reading scores for fourth-grade children has a mean of 25 and a standard deviation of 5. A set of scores for...
5. ### Standard normal distribution

Can someone please help me answer this Q with workings so I learn? Using a survey in winter 2009, it was estimated only 1% of households have solar panels to generate electricity. Consider a random sample of 20 houses. a) What is the probability that none of them have solar panels to...
6. ### sum of truncated Normal Variables

Hello all, I am trying to find if there exists a closed solution for the following: X~N(u,var) {normal dist) Y~N((u,var)|Y>a) {truncated normal dist} Z1=X+Y Is Z distribution is known? Thanks, Alon
7. ### Estimating parameters of simulated Normal Data sets

Dear Sir/Madam, I am doing a simulation study. For my study, I need to simulate 10,000 data sets from standard normal distribution(each with 100 observations) and need to estimate the mean and standard deviation parameters of all 10,000 data sets. I used replicate function to generate...
8. ### Probability that one random variable is greater than another

I need to find the probability that a normally-distributed random variable is greater than a uniformly-distributed random variable. That is: X \sim \mathcal{N}(\mu, \sigma^2) Y \sim \mathcal{U}(0, 1) What I'm looking for is: Pr(X \ge Y). I got this thus far, but I'm not sure it's right, and...
9. ### Is this a correct statement regarding a normal distribution?

Note: this is not homework. I am trying to make sure I understand the differences between percentiles and z-score. Please tell me if the following compare/contrast statements are correct. Thanks, Mike 1. The 95th percentile is the value such that 95% of all observations are below...
10. ### Standard Normal random variable problem: I have no idea on how to start...

Assume X is a standard normal random and Y ~ N(0,9). What is the 97.5 percentile of p(X) and p(Y)?
11. ### need help mean and varience

Let X1, X2, …., Xn, and Y1, Y2, ….Yn be 2n observations from a population with mean µ and variance σ2=1. Consider: An = ((X1+X2+⋯.+Xn)- (Y1+Y2+⋯..+Yn))/n Compute the mean and the variance of (√n)An i got following x bar - y bar approach normal (M1 - M2 , 1/n + 1/n)
12. ### R <-> Matlab, generating correlating normal variates

R <-> Matlab, generating correlated normal variates HI, I need to generate correlated normal variates, with certain mean and sd. I don't have Statistics Toolbox, so I have to code it myself. I have a running R code from: http://www.unt.edu/benchmarks/archives/2001/december01/rss.htm but...
13. ### confusion on terminology

I could use some confirmation or correction on something basic that has been confusing me for a while. It has to do with "normal" and steps in modeling. Normality is for residuals (people already helped me with this in a previous thread) and this comes after fitting a model. In the beginning of...
14. R

### Transforming Variables

I have several different variables. The majority of the variables were positively skewed and therefore I did a log10 transformation to make them more normal. However, two of the variables were quite normal already and now after log10 are more negatively skewed. In order for me to do some...
15. ### Normal Probability Distribution

In 2010, the population of SAT scores were normally distributed with a mean of 1020 (reading and math only) and a standard deviation of 200. The NCAA requires Division I athletes to score at least 820 to compete the first year. A random sample of 4 students is gathered. What is the probability...