Normal distribution Definition and 240 Threads

Homework Statement The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with a mean μ, the actual temperature of the medium, and standard deviation σ. What would the value of σ have to be to ensure that 95% of all readings are within 0.1...

The fisher information matrix for multivariate normal distribution is said at many places to be simplified as: \mathcal{I}_{m,n} = \frac{\partial \mu^\mathrm{T}}{\partial \theta_m} \Sigma^{-1} \frac{\partial \mu}{\partial \theta_n}.\ even on...

If the banker's offers were equal to the expected value of the remaining cases, would the offers be normally distributed? I'd say the answer is yes. Take a roll of a die, for instance. Die rolls are normally distributed, with a mean of 3.5 and a standard deviation of 2 11/12.

Hello to all. Simple question but I'm getting the wrong answer here. Question: The random variable X is normally distributed with mean μ and variance 21.0. Given that P(X > 10.0) = 0.7389, find the value of μ. The equation we'll use is thus: z=(x-μ)/SD So, what I did was: 0.64...

Hi, I'd like to know the value that \Phi(x) of a normal distribution is approximated when x> 3,5. I assume it is 1, since the value for x=3,49 is 0,9998... But I got some answers at the university that it might be 0,5 Thanks

Homework Statement A high jumper knows from experience that she can clear a height of at least 1.78m once in 5 attempts. She also knows that she can clear a height of at least 1.65m on 7 out of 10 attempts. Find to 3 dp the mean and standard deviation of the heights the jumper can reach...

Question : Random variate X follows a normal distribution with mean 0 and variance 1 i.e.X~N(0,1). Given Y = 2X + 4, find i) E[Y] ii) Var(Y) iii) E[X^3] Solution: here E[X'] = 0 and V(X) = 1 i) E[Y] = E[2X+4] = 4 [Is this correct] ii) Var(Y) = E[Y2] - [E(Y)]2 =E[Y2] -16...

Question: The diffusivity (D) of water in cells is about 0.025 meters/seconds^2 If I know that the diffusion will occur over 100 milliseconds (mS), what is the standard deviation of the normal distribution of diffusion that occurs during that timeframe. It seems to me that it is...

Hello! Would someone or several people mind posting a link to a coherent derivation of the normal distribution? Assume that the person reading it is a total moron with a multivariate calculus and AP Statistics background. I've already looked at the top google results, so save yourself the...

Test scores on a standardized test have mean 55 and variance 64. What is the probability that a random sample of 256 scores will have a sample mean score between 53 and 57 I attempted the problem and came up with this: u=55 and sd = 8 (Square root of 64) \mu=55 \sigma=\sqrt{64}=8 P(53<...

If I had Z=Y^3 where Y is a standard normal distribution. How would I approx. calculate the probability of Z<=1 ?, I would understand it if it was Z=Y^2 which is chi-square...

Hi All, I'm wondering if ln(x) has any know distribution when x is a normal random variable? Also, is there any distribution for x that generate a known distribution for ln(x)? Thanks,

Suppose that the height of adult females in a population is a normal random variable with a mean of 165 cm and a standard deviation of 12 cm. If heights are measured to the nearest centimetre, what percentage of the adult female population will have a measured height between 150 and 160 cm...

Homework Statement Find the Z value that corresponds to the given area. http://img163.imageshack.us/img163/3785/problem1v.jpg The Attempt at a Solution What I did was go to Table E and find the closest number to 0.0166 which was 0.0160, and the Z numbers were 0.04 and 0.0. I then added them up...

Hi all, When working out confidence intervals based on population samples are you supposed to always use t-distributions, standard normal (z) distributions, or do you make a choice based on the sample size? Up until now I've been lucky enough to have large sample sizes (for some work I'm...

I am a bit confused with the notation, Whenever I see N(mu,alpha) does that mean the data set is normal and does it also mean that it's standard normal? Is there a difference between using Z~N(mu,alpha) vs. X~N(mu,alpha)? does the Z indicate standard normal?, if so why don't we just use...

I have a set of data that I used to create a histogram, and would like to fit it with a Gauss shape...I used the regular equation for a normal distribution, using the mean value and the standard deviation of my data, but the Gauss shape doesn't seem to be really fitting my data... I might be...

Z=(-1/sqrt(n)) * sum from k=1 to n of [1+log(1-Fk)] Fk is a cumulative distribution function which is continious and strictly increasing. Show that as n->infinity, Z converges to a normal distribution with mean 0 and var 1 --------------------- From Taylor series, log(1-x) = -sum...

Hi Everyone, Question: Mean is 0.252, standard deviation is 0.003, permitted tolerance of 0.246 to 0.258. What percentage of washers will be discarded. Attempt: I am so stuck. I have looked at my text and online for hours and know that it should be fairly easy but I am getting stuck...

Please try this question and see whether you got my answer...i am having some doubt The random variable X is normally distributed with mean V and variance C^2. It is known that P(x>102)=0.42 and P(x<97)=0.25 calculate V(mean) and variance c^2 i got mean 100.8 and variance(-5.7)^2

Homework Statement A manufacturing plant utilizes 3000 electric light bulbs whose length of life is normally distributed with mean 500 hours and standard deviation 50 hours. To minimize the number of bulbs that burn out during operating hours, all the bulbs are replaced after a given period...

Homework Statement The time until the first failure occurred in supplies ink to a particular printer brand, follows a normal distribution with μ=1500 and standard deviation(σ) 20 hours of operation. What percentage of these printers will be damaged before the end of 1000 hours of operation...

If anyone could help me with the following Q it would be much appreciated! Womens weights - N (68kg, (18)^2 kg) Mens Weights - N (82kg, (15)^2 kg) Mary and Jon are sailing a raft. Marys equipment weights 20% of her weight. Jons weighs 50% of his weight. The raft will sink if the total...

3. A local manufacturer creates distress flares. The times the flares last are normally distributed with a mean life of 9.8 years and a standard deviation of 1.3 years. (b) A small boat owner who regularly travels out to sea wants to be sure his distress flare works. Determine when he should...

Hello, Where does the standart normal distribution function \Phi (x)=\frac{e^{-\frac{x^2}{2}}}{\sqrt{2\pi }} come from?I wonder it.Please explain to me.Thanks for your helps.

Homework Statement A plant manufactures 500 components a day with the diameter being random variable: N(8.02, 0.1^2)mm What is the probability of two randomly picked components differing by more than 0.3mm?2. Solution I know that the solution is 0.966The Attempt at a Solution I thought that I...

Homework Statement One sixth of the male freshman entering a large state school are out of state students. If the students are assigned at random to the formitories, 180 to a building. 1) What approximately is the probability that in a given dormitory at least one fifth of the students are...

Homework Statement A study investigates the performance of students in an exam, which is known to follow a normal distribution, with a mean of 63 and a standard deviation of 21. What is the probability that the difference between two randomly selected students is more than 5 marks...

I have been puzzling over this problem for about a week now and cannot find the answer. In my opinion it is very theoretical, but I know I ma not the best mathematician on here so maybe someone else could look at this. Thank you.

Homework Statement A cola company's long-term market share is estimated to be 45%. After an extensive advertising campaign, 68 out of 150 customers surveyed claimed to have purchased this company's cola recently. Was the advertising campaign a success? justify your assessment Homework...

I am trying to create a calculator that let's a user provide the standard deviation, mean, frequency at that mean, and range of values - then the calculator will give the frequency in that value range. For instance, purely illustrative -- say you know the mean weight for some group is 100kg...

What properties does some measurement possesses such that they fit along a normal curve? And how was the general formula found? Wikipedia says very little on this.

suppose that X is normally distributed with mean u and standard deviation sigma. show that var(x)=sigma^2.[you many use the fact that if Z is standard normally distributed, then EZ=0 and var(x)=1]

suppose that f(x) is the density function of a normal distribution with mean u and standard deviation sigma. show that u= intergral from -infinity->+infinity xf(x)dx

Hi all, I have a stats problem I'm trying to figure out. Suppose I have a very large population (~millions) of colored balls with exactly 50% red, 30% green, 20% blue. If I take a random sample of 1000 of these balls, the distribution of colors I end up with can be modeled as a multivariate...

Been having an issue with these specific homework problems. Can you give me some insight on where to start. #4.78 F The actual amount of juice that a machine fills the juice boxes with is 4-ounces, which may be a random variable with normal distribution of \sigma = 0.04 ounce a) If only 2%...

Homework Statement You measure the weight of each walnut in a big bag of walnuts and find that the probability distribution of walnut weight is a normal distribution with a mean weight <W> = 30 grams and a standard deviation σW = 5 grams. What is the probability that two randomly chosen...

Homework Statement http://img16.imageshack.us/img16/7703/ass1lx.jpg Homework Equations The Attempt at a Solution I know that f(x_1, x_2, x_3) = \frac{1}{(2 \pi)^{3/2}|\Sigma|^{1/2}}exp(-\frac{1}{2}x \Sigma^{-1} x) since n = 3 and mu = 0. I've never used the multivariate...

Hi, everyone, I have a quick question for normal distribution in Excel. There's a construction project with the following monthly expenditures: JUL 2008 $ 4,903 AUG 2008 $ 3,591 SEP 2008 $ 15,452 OCT 2008 $ 12,806 NOV 2008 $ 59,988 DEC...

Homework Statement Which of the following is/are likely to show normal distribution? A) Numbers of cervical vertebrae in different species of mammals B) Age distribution of children in school C) Number of fruits in mango trees in an orchard D) Fasting blood glucose levels of healthy people...

If the covariance matrix \mathbf{\Sigma} of the multivariate normal distribution is invertible one can derive the density function: f(x_1,...,x_n) = f(\mathbf{x}) =...

Homework Statement Assume x is normally distributed with a mean of 5 and standard deviation of 4. Determine value of x that solves: P(-X<x-5<X) = .99 Homework Equations I have been using normalCDF and inverse functions on the TI-84 to solve, and I understand how to do these without the...

Homework Statement Let the probability density function of X and Y be bivariate normal. For what values of a is the variance of aX+Y minimum? Homework Equations The answer in the book is -p(X,Y)(std dev of X/std dev of Y) The Attempt at a Solution I think the equation for...

Homework Statement In considering the safety of building, the total force acting on the columns of the building must be examined. This would include the effects of the dead load, D, due to weight of the structure, the live load, L, due to human occupancy, movable furniture and the like, and...

Homework Statement 3 (a) A sample of 50 washed baking potatoes was selected at random from a large batch. The weights of the 50 potatoes were found to have a mean of 234 grams and a standard deviation of 25.1 grams. Construct a 95% confidence interval for the mean weight of potatoes in...

Statistics Question - Normal Distribution SOLVED Homework Statement Hey, the question is shown in the attached document. Homework Equations Mean = 79 Standard Deviation = 12 The Attempt at a Solution I dispise these questions, and I'm failing to grasp them at all. I've done...

hey I am 16, grade 12 in australia, struggling on the hardest question on the current maths assignment. i was wondering if someone could point me in the right direction? i really have no idea where to start. and no one i seem to ask has any useful info. Homework Statement...

Homework Statement Assume X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the value for x that solves P(-x < X - 10 < x) = 0.95 Homework Equations P(X < x) = P(Z < z) = P(Z < (x - mean)/stdev) The Attempt at a Solution P(10 -x < X < 10 + x)...

Homework Statement Assume X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the value for x that solves P(x < X < 10) = 0.2Homework Equations P(X < x) = P(Z < z) = P(Z < (x - mean)/stdev) The Attempt at a Solution P(X < 10) - P(X < x) = 0.2 P(Z <...

Hello again So we are studying the gaussian normal distribution and what I understand about it is that it helps picture many of the natural phenomena where the basica idea is probabilities are equally distributed around the average. I understand that the e^-x^2 term in the formula ensures the...