Answered: uppose x has a distribution with a mean…

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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Suppose x has a distribution with a mean of 40 and a standard deviation of 21. Random samples of size n = 36 are drawn.

a) Describe the x̅ distribution.

x̅ has a geometric distribution

x̅ has a Poisson distribution.

x̅ has an unknown distribution

x̅ has a normal distribution

x̅ has an approximately normal distribution

x̅ has a binominal distribution

Compute the mean and standard deviation of the distribution. (For each answer, enter a number)

ux̅ =

ox̅ =

b) Find the z value corresponding to x̅ = 47 (Enter an exact number)

z =

c) Find P(x̅ < 47) =

d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 47?

Yes, it would be unusual because less than 5% of all such samples have means less than 47

Yes, it would be unusual because more than 5% of all such samples have means less than 47

No, it would not be unusual because more than 5% of all such samples have means less than 47

No, it would not be unusual because less than 5% of all such samples have means less than 47

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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