Answered: A variable of a population is normally…

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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A variable of a population is normally distributed with mean µ and standard deviation σ. For samples of size n, fill in the blanks. Justify your answers.

a. Approximately 68% of all possible samples have means that lie within of the population mean, µ.
b. Approximately 95% of all possible samples have means that lie within of the population mean, µ.
c. Approximately 99.7% of all possible samples have means that lie within of the population mean, µ.
d. 100(1 - a)% of all possible samples have means that lie within of the population mean, µ. (Hint: Draw a graph for the distribution of x, and determine the z-scores dividing the area under the normal curve into a middle 1 - a area and two outside areas of a/2.)

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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