Answered: Suppose x has a normal distribution…

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 normal distribution with mean μ = 50 and standard deviation σ = 11.

Describe the distribution of x values for sample size n = 4. (Round σ_x to two decimal places.)

μ_x	=
σ_x	=

Describe the distribution of x values for sample size n = 16. (Round σ_x to two decimal places.)

μ_x	=
σ_x	=

Describe the distribution of x values for sample size n = 100. (Round σ_x to two decimal places.)

μ_x	=
σ_x	=

How do the x distributions compare for the various samples sizes?

The means are the same, but the standard deviations are decreasing with increasing sample size.The means are the same, but the standard deviations are increasing with increasing sample size. The means and standard deviations are the same regardless of sample size.The standard deviations are the same, but the means are decreasing with increasing sample size.The standard deviations are the same, but the means are increasing with increasing sample size.

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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