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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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.)

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