Suppose x has a distribution with μ = 26 and o = 18.(a) If a random sample of size n = 34 is drawn, findprobability to four decimal places.)Mx =USE SALTo x =P(26 ≤ x ≤28) =MXX(b) If a random sample of size n = 65 is drawn, find µ, o and P(26 ≤ x ≤ 28). (Round o to two decimal places and theprobability to four decimal places.)=MX²0 and P(26 ≤ x ≤ 28). (Round o to two decimal places and theXo x =P(26 ≤ x ≤28) =

Given,Mean(μ)=26standard deviation(σ)=18

Answered: Suppose x has a distribution with = 26…

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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Let X1 and X2 be observations of a random sample of size n = 2 from a Cauchy Distribution.Find P(X1 < −1 and 1 < X2)
Suppose x has a distribution with μ = 24 and σ = 18. (a) If a random sample of size n = 41 is drawn, find μx, σ x and P(24 ≤ x ≤ 26). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(24 ≤x≤ 26) = (b) If a random sample of size n = 63 is drawn, find μx, σ x and P(24 ≤ x ≤ 26). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(24 ≤ x ≤ 26) =
Suppose x has a distribution with μ = 11 and σ = 3. If a random sample of size n = 62 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σ x to two decimal places and the probability to four decimal places.)μx = σ x = P(11 ≤ x ≤ 13) =
2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.
1a) Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample.n = 100, p = 0.32: P(X < 34) b) A mail-order company has a 9% success rate. If it mails advertisements to 500 people, find the probability of getting fewer than 38 sales. c) Find the critical value zα/2 needed to construct a(n) 99.2% confidence interval. Please answer all parts of the question 1a to 1c. Thanks.
When taking random samples of n observations from a population that is not normally distributed, the sampling distribution, x, will be approximately normally distributed never. The population itself must be normally distributed for x to be normally distributed. when the population distribution has low kurtosis. always. when the population standard deviation, o, is greater than n. when n is sufficiently large.
Suppose x has a distribution with u = 29 and o = 25. (a) If a random sample of size n = 43 is drawn, find u, o , and P(29 < x < 31). (Round o, to two decimal places and the probability to four decimal places.) 0こ= P(29 < x < 31) = (b) If a random sample of size n = 61 is drawn, find u, o y and P(29 < x < 31). (Round o , to two decimal places and the probability to four decimal places.) 長= 『ス= P(29 < x < 31) =
Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributed
6. Choose 2 points (X, Y) uniformly at random from the circle. Find the expected area of the rectangle with opposite corners given by X and by Y.
Suppose x has a distribution with = 12 and a = 6. USE SALT (a) If a random sample of size n = 41 is drawn, find , and P(12 sx s 14). (Round to two decimal places and the probability to four decimal places.) H-12 0.93 X P(12 ≤ x ≤ 14)= 0.4842 X (b) If a random sample of size n = 68 is drawn, find and P(12 sxs 14). (Round a to two decimal places and the probability to four decimal places.) H-12 ✓ 1.33 x P(12 sxs 14)=0.4337 X (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is smaller than part (a) because of the larger ✔✔sample size. Therefore, the distribution about is wider ✓x

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