Which of the following statements are TRUE about the normal distribution? Check all that apply.A z-score is the number of standard deviations a specific data value is from the mean of the distribution.The area to the left of a z-score plus the area to the right of that same z-score will always equal 1.The mean corresponds to the z-score of 1.The Empirical Rule only applies when a value is exactly 1, 2, or 3 standard deviations away from the mean.A data value with z-score = -1.5 is located 1.5 standard deviations below the mean.

Here the given statements are verified with properties of normal distribution.

Answered: Which of the following statements are…

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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Which of the following statements are TRUE about the normal distribution? Check all that apply.

A z-score is the number of standard deviations a specific data value is from the mean of the distribution.
The area to the left of a z-score plus the area to the right of that same z-score will always equal 1.
The mean corresponds to the z-score of 1.
The Empirical Rule only applies when a value is exactly 1, 2, or 3 standard deviations away from the mean.
A data value with z-score = -1.5 is located 1.5 standard deviations below the mean.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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