Answered: Why is it correct to say "a" normal…

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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Why is it correct to say "a" normal distribution and "the" standard normal distribution?

Describe the cases in which the different terms are used. Choose the correct answer below.

"The" standard normal distribution is used to describe one specific normal distribution

(μ=0, σ=1).

"A" normal distribution is used to describe a normal distribution with any mean and standard deviation.

"The" standard normal distribution is used to describe the normal distribution with any mean and standard deviation. "A" normal distribution is used to describe one specific normal distribution

(μ=0, σ=1).

"The" standard normal distribution is used in cases where all of the data values are known (population). "A" normal distribution is used in cases where only a portion of the data is known (sample).

There is no difference between "A" and "The" normal distribution. The terms can be used interchangeably.

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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