MathStatisticsQ&A LibraryA 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.)

Question

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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