Answered: a) A given distribution has a…

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) A given distribution has a population mean, μ, of 106 and a population standard deviation, σ, of 8. What z-score would be associated with the value x = 140?

b) A given distribution has a population mean, μ, of 138 and a population standard deviation, σ, of 11. What z-score would be associated with the value x = 98?

c) A given distribution has a population mean, μ, of 143 and a population standard deviation, σ, of 5. Compute the raw, x-value associated with a Z-score of -2.02.

d) A given distribution has a population mean, μ, of 110 and a population standard deviation, σ, of 11. Compute the raw, x-value associated with a Z-score of 1.12.

e) Suppose a population is known to be normally distributed with a mean, μ, equal to 116 and a standard deviation, σ, equal to 14. Approximately what percent of the population would be between 88 and 130?

f) Suppose a population is known to be normally distributed with a mean, μ, equal to 116 and a standard deviation, σ, equal to 14. Approximately what percent of the population would be between 88 and 116?

g) Suppose a population is known to be normally distributed with a mean, μ, equal to 116 and a standard deviation, σ, equal to 14. Approximately what percent of the population would be between 102 and 130?

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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