Scores on a certain standardized test, IQ scores, are approximately normallydistributed with mean μ = 100 and standard deviation o=15. Here we are referring tothe distribution of scores over a very large population, and we approximate thatdiscrete cumulative distribution function by a normal continuous cumulativedistribution function.(a) An individual is selected at random. What is the probability that his score Xsatisfies 120 < X < 130?(b) Two individuals are selected at random, independently. What is the probabilitythat their scores X and Y satisfy max (X,Y) > 120?

Answered: Image /qna-images/answer/18c78aba-5414-418c-9228-61fc43db96ca.jpg

Answered: Scores on a certain standardized test,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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If there is an association between two variables, which is true? 1- the scores of the cases are approximately equal 2- the distributions of the scores approach normality 3- all of the scores are in the same row in the bivariate table 4- the conditional distributions of Y change
26 The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α=0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.37 0.75 0.60 0.49 2.66 1.18 0.33 0.46 0.46 1.64 0.33 0.50 0.58 0.41 1.39 (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region. The degrees of freedom for the numerator, d.f.N, is ____ and the degrees of freedom for the denominator, d.f.D, is _____ The critical…
Suppose an x distribution has mean μ = 2. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81. (a) What is the value of the mean of each of the two x distributions? For n = 49, μ x = For n = 81, μ x = (b) For which x distribution is P( x > 2.5) smaller? Explain your answer. The distribution with n = 49 because the standard deviation will be smaller.The distribution with n = 81 because the standard deviation will be smaller. The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 81 because the standard deviation will be larger. (c) For which x distribution is P(1.5 < x < 2.5) greater? Explain your answer. The distribution with n = 49 because the standard deviation will be larger.The distribution with n = 49 because the standard deviation will be smaller. The distribution with n = 81 because the standard deviation will be…
#6
Q.6 (a) Write the gamma distribution for a random variable X denoted by X~F(a, B); its mean, variance and moment generating function (No derivation is required). (b) What is the relationship between gamma distribution and chi-square distribution?
You take a simple random sample of size 25 from a very large population in which the true proportioni p=0.1. Which statement below best describes what you know about the sampling distribution of p? (0.1)(0.9) (a) H,-0.1; o,- the distribution is skewed right. 25 (0.1)(0.9). 25 (b) H,=0.1; o,=. ; the distribution is skewed left. (0.1)(0.9). (c) ,=0.1; o,= the distribution is approximately Normal. %3D 25 (0.1)(0.9) (d) , the distribution is not approximately Normal. 25 =0.1; we cannot use the formula o, (0.1)(0.9) ; the distribution is approximately Normal. 25 (e) =0.1; we cannot use the formula o,
A,b,c,d.
Your income (.) per month is a Gaussian random variable with mean 2990 NIS and standard deviation 240 NIS. Your monthly expenditure (ia) also follows the Gaussian distribution with mean 2400 NIS and standard deviation 270 NIS. TABLE CTICAL VALINS TUDENS DSTRIBUTION Chi Styue atrihaxe Tali Find the probability that in a given month you will be able to save (i) at least 1000 NIS. [The answer should be a number rounded to five decimal places, don't use symbols such as %] E 明中非非

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How do you find the mean and variance of part(d)?I need the detailed solution.
For the questions below, please show the derivation of the distributions step by step. (a) Suppose that the random variables X₁,..., X, form a random sample from a standard normal distribution. Let (b) Y = (X₁ + X₂ + X₂ + X₁)² + (X₂ + X6 + X₁ + X)². Obtain the c value so that the random variable cY has a x² distribution. Suppose that X₁,..., X, are independent and identically distributed random variables from a standard normal distribution. Obtain the value of d so that the random variable has at distribution. d(x₁ - + X₂ + X₂) (X₂²+X₂²+X₂² X,²)/² (c) If S and S are the variance for the sample of independent random variables with size n₁ = 6 and n₂ =10, taken from a Normal distribution with common variance, calculate the value of e so that P(S²/S2
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr

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