Normal distribution Definition and 240 Threads

Is there a relationship between QM probability and normal distribution ? I'm thinking about drawing probability densities as functions of phase. Thanks

The lengths of a certain species of worm follow a normal distribution. Thirty percent of the worms are at least 16cm long, and 15% of the worms are less than 10cm long. Find, to 2 decimal places, the standard deviation of the lengths of the worms.

How is the expected frequency column worked out for each interval of trains? 2) My attempt Take the first interval, 60 - 62, I thought about doing this: (62 - mean) / standard deviation (62 - 67.45) / 2.92 = - 1.866 using Z score < - 1.886, from the normal distribution table, I get: 1 -...

I need help understanding normal distribution. I am self studying statistics to help me in my role of teaching excel as a business tool. I understand taking a data set and creating a frequency distribution. I don't understand about normal distribution. Why should any data set regardless of...

I am preparing for my math probability class next semester. There is question: Calculate E(x3µσ) Would anyone explain the solution in the picture a little bit to me? 1.Why is the step hold? Is there a formula or something that i can calculate E[X-µ]n? 2.Why is the fourth step hold? Where is...

Homework Statement Due to the pollution from the industry around an apple farm, the apples grown there may be contaminated by heavy metals. It is believed that the amount of heavy metals in an apple of the farm follows the Normal distribution. N(16,16) which has a mean μ = 16 units and σ = √16...

Does anyone know the proof of joint moment generating functions for bivariate normal distributions? M_x,y (s,t)= E(e^(xs+yt))

Homework Statement Suppose that diastolic blood pressures (DBPs) for men aged 35-44 are normally distributed with a mean of 80 (mm Hg) and a standard deviation of 10. What's the probability that in a random sample of 5 subjects, 4 or more have DBPs more than 90? Homework EquationsThe Attempt...

Hi comunity! I need to make a code o a normal distribution of velocities, starting whit a random secuence uniformly distributed between [0,1]. I am using FNT95, with Plato. I want to obtain a ''for'' bucle with I=1,N for the velocities. It is importan for the distribution to have sigma defined...

Given five data points (minimum, 25th percentile, 50th percentile, 75th percentile, maximum), do I have enough information to be able to construct what a normal (Gaussian) distribution would look like? I have no data on any other statistical information (population size, mean, median, mode...

Homework Statement Find P(X>130) where P(X > 130) = 1 − Φ( (130 − µ)/σ ) Homework Equations Φ is the normal distribution density function: http://en.wikipedia.org/wiki/Normal_distribution The Attempt at a Solution This is pretty simple to use in R if one knew how to. I get a ghastly incorrect...

Homework Statement I have to prove that ## \int e^{\frac{x^2}{-2}}dx ## from +∞ to -∞ = ##\sqrt{2\pi} ## Homework Equations N/A The Attempt at a Solution My GSI went from 1) ## \int e^{\frac{x^2}{-2}}dx ## from +∞ to -∞ = ##\sqrt{2\pi} ## to 2) ## (\int e^{\frac{x^2}{-2}}dx)(\int...

Hello, I have two jobs,Normal distribution with mean of 4.5 minutes and standard deviation of 1.5 minutes for type 1 and uniformly distributed between 1 and 3 minutes for type 2

Let X be random variable and X~N(u,σ^2) Thus, normal distribution of x is f(x) = (1/σ*sqrt(2π))(e^(-(x-u)^2)/(2σ^2))) If we want to standardize x, we let z=(x-u)/σ Then the normal distribution of z becomes z(x) = (1/σ*sqrt(2π))(e^(-(x^2)/(2)) and we usually write Z~N(0,1) But as you can see...

Homework Statement $$f:\mathbb{R} \rightarrow \mathbb{R},$$ $$ f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-(x-\mu)^2}{2 \sigma ^{2}}}$$ What are the roots of this equation? Homework EquationsThe Attempt at a Solution The roots of an equation are the values of x such that f(x) = 0. This...

Okay, so I guess my first question is if the main utility of the normal distribution ##f(x)## is to provide a probability measure for any subspace of the measurable space ##(\mathbb{R},\mathcal{B})## (where ##\mathcal{B}## is the borel σ-algebra on the real numbers) by defining the measure as...

Homework Statement My source textbook is the community college / junior college (confer: undergraduate-lower division) probability and statistics textbook: An Introduction to Mathematical Statistics and Its Applications, 2nd Edition Authors: Richard J. Larsen, Morris L. Marx 1986...

I have ##\bar{X}## ~ ##N(\mu , 9/25)## I have ##E[X] = \mu## ##Var[X] = 9/25## ##SD[X] = 3/5 = 0.6## An interval for ##\bar{X}## has been recorded: ##\bar{X} \pm 1.05##. I asked to find ##P(\bar{X} > \mu + 1.05)## I can "normalize" the distribution through: ##Z =...

Lets say I have 8 samples (weight) of 4 ingredients in particular food by X brand and another 8 samples by Y brand. I would like to test to see if there is any difference between the two brands in terms of weight of particular ingredients. However, I am not sure what statistic test to run and I...

Homework Statement "Cans of lemon juice are supposed to contain 440 ml of juice. It is found that the actual volume of juice in a can is normally distributed with mean 445 ml and standard deviation 3.6 ml." It is found that 94% of the cans contain between 445−c ml and 445+c ml of juice. (ii)...

Homework Statement Two independent series of experiments are performed. The probability of a positive result (independent of each other) in the respective series are given by p and q. Let X and Y be be the amount of experiments before the first negative result occur in the respective series...

Homework Statement Let X1,X2,X3 be a random sample from a normal distribution with mean μ≠0 and variance σ2=1/24. What are the values of a and b, respectively, in order for L=aX1+4X2+bX3 to have standard normal distribution?Homework Equations σ=1/√24 Converting normal distribution to...

If ( X,Y ) has the normal distributions in two dimensions with zero means and unit variances and the correlation coefficient r, then how to prove that the expectation of the greater of X and Y is \sqrt{(1-r)\pi}?

Homework Statement A machine fills cereal boxes, normally distributed, with standard deviation of .1 oz. What amount setting should the machine be set to if only 1% of the boxes can have less than 16oz of cereal? Homework Equations The Attempt at a Solution I am thinking that I...

I have a final exam in probability and I faced a question that made me think of the logic and the concept of the normal distribution. Here is the question: A food industry company imports oil in big tanks and refills bottles of different sizes with it. One of the main filling sizes is the...

If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution? I tried to do this with the sum of bernouli variables and...

I have done 3 experiments. For each one of them, I have repeated the same experiment 100 times. Which gives me three sets of 100 numbers. Experiment 1: for number 30 ---> 100 results Experiment 2: for number 40 ---> 100 results Experiment 3: for number 50 ---> 100 results Basically, I...

Hi I read at this link http://www.eecs.berkeley.edu/~aude/papers/TRB2012_stat_traffic.pdf something like bus travel times can be normally distributed. Sounds strange to me because normal distribution presumes even negative values Anything I am missing here? Regards

Homework Statement X refers to score distribution in Math and Y refers to score distribution in Stat in a certain degree course exam. It is known that X~N(mean = 62, sigma=7) while Y~N(mean = 68, sigma=10). If X and Y are independent, find (i) P[X+Y>120]; (ii) P[X<Y]; (iii) P[X+Y>140]...

Homework Statement (Page 222 number 5) A highway department has enough salt to handle a total of 80 inches of snowfall. Suppose the daily amount of snow has a mean of 1.5 inches and a standard deviation of .3 inches. Approximate the probability that the salt on hand will suffice for...

I was reading this problem on calculating the probability of hitting a certain region on a dartboard. The number of hits the dart thrower will land at a certain radius R on the dartboard is proportional to e^(-R^2). The task is to take a certain portion of a ring (or annulus) on the dartboard...

1) For the normal distribution it seems that the integral of the propability density function from \mu-\sigma to \mu+\sigma is independent of \sigma. I guess that gives kind of a nice interpretation of \sigma. But how do you prove this, when the antiderivative of an exponential with a square...

Homework Statement Metal strips are produced mean length 150cm, standard deviation 10cm. Find probability that length of random strip is: a/ shorter than 165cm b/ longer than 170cm c/ between 145 and 155cmHomework Equations Z = x - μ / σ θ (Z) - θ (z) = average probability (question c) The...

bivariate normal distribution-"converse question" Hello, I have a theoretical question on how to use the bivariate normal distribution. First I will define what I need, then I will ask my question. pics from: http://mathworld.wolfram.com/BivariateNormalDistribution.html We define the...

Let X be normally distributed with \mu =100cm and \sigma =5 cm (a) shade region P(X>105) https://www.physicsforums.com/attachments/1010 (b) Given that P(X<d)=P(X>105), find the value of d. wasn't sure if this meant that d is the left of 105 which would be larger in volume than X>105

I am trying learn how to graph Normal distribution with TI-Nspire CX CAS went to the Ti.com but just found a work sheet. or else I missed it some where. but saw some examples on the display. thanks ahead for help:cool:

Hey all. I'm working on a personal programming project where I'm attempting to simulate (to a small degree) a galaxy. And I have come across a decent 2D density map for a spiral galaxy. This map (array actually) defines a 128x128 grid of values between 0 and 255 representing the frequency of...

Homework Statement We have two normally distributed random variables: A = N(129, 29.4) B = N(86, 24.0) What is the probability A is atleast twice the size of B? The Attempt at a Solution P(A > 2B | B = b) or something? I think we are supposed to use the CLT somehow but I don't...

Homework Statement Show that there is no minimum for the normal distribution function e^(-(x-μ)^2/(2 σ^2))/(sqrt(2 π) σ) Homework Equations The Attempt at a Solution I figured I'd take the derivative and set it equal to 0, but then what?

Homework Statement Suppose X is a normally distributed random variable. Suppose also that P ( X > 44.7 ) = 0.33 and P ( X < 46 ) = 0.7123. What is the mean and standard deviation of X ? Homework Equations The Attempt at a Solution P(X<44.7) = 1-P(X>44.7) = 1-.33 = .67 P(X<44.7)...

Homework Statement A biologist interested in the mass of Chickadees (Poecile atricapillus) in North Glenmore Park collects the 3 samples shown below: Sample 1: 9 individuals with a mean mass of 13.23 grams Sample 2: 16 individuals with a mean mass of 9.64 grams Sample 3: 13 individuals...

Homework Statement Variable A has mean 55 and variance 9, variable B has mean 65 and variance 25. If A and B are normally distributed, find P (B > A) Homework Equations z = (x - μ) / σ The Attempt at a Solution Can this be solved? What is the meaning of P (B > A)? The probability...

Homework Statement Given: Standard Deviation = 500 Homework Equations How I calculate the μ (mean) using standard deviation for a norma distribution. Thanks. The Attempt at a Solution

Homework Statement Generalize: For arbitrary 0 < p < 1, show that the method giving a and b produces the minimum length interval. Hint: It might be helpful to use local extrema for the inverse function of the distribution function. Homework Equations The method is is talking about is...

Homework Statement Question - On a statistics examination, the mean was 78 and the standard deviation was 10. (assume normal distribution). a) Find the standard scores of two students whose grades were 93 and 62, respectively. b) Determine the grades of two students whose standard...

Scope of this thread is to give a complete as possible answer to the question proposed two days ago by the user simon11 on Basic Probability and Statistic forum... Assume two random variables X and Y are not independent, if P(X), P(Y) and P(Y|X) are all normal, then does P(X|Y) also can only be...

Hello, I'm David. I'm a new member here. Could anyone of you help me? Where can i find the formal deduction of Gauss' Normal Distribution Function? I've read a lot of statistics books and never found that. Where that comes from? It's just curiosity, not homework. P.S.: sorry about my...

Assume two random variables X and Y are not independent, if P(X), P(Y) and P(Y|X) are all normal, then does P(X|Y) also can only be normal or not necessarily? thanks.

Homework Statement Let N(x) denote the CDF of the standard normal density. So, it's the integral of the standard normal density from -∞ to x. Is it true that \lim_{b\to 0} N(\frac{a}{b}) = N(\frac{a}{\lim_{b\to 0}b}) = N(+\infty) = 1? 2. The attempt at a solution This is more of a...

Homework Statement find the normal approximation for the binomial probability P(x = 4,5) where n=14 and p = .5. Homework Equations μ = np σ = sqrt(npq) z = (x - μ)/σ The Attempt at a Solution p = .5 q = .5 μ = 14*.5 = 7 σ = sqrt(14 * .5 * .5) = 1.87 z = (4 - 7)/1.87...