Answered: Consider the normal distribution…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter7: Applying Fractions

Section7.6: Percents Problems

Problem 10WE

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Consider the normal distribution represented by the normal curve in the figure to the right. (Assume the two labeled values are equidistant from the mean.) Complete parts (a) and (b) below.

A normal curve is over a horizontal axis and is centered at the mean. Vertical line segments extend from the horizontal axis to the curve at 80.6, the mean, and 99.4, where 80.6 is to the left of the mean and 99.4 is to the right of the mean. The area under the curve between 80.6 and 99.4 is shaded and contains 95 percent of the data.80.699.4

(a) Find the mean

and standard deviation

of the distribution.

μ=nothing

cm (Simplify your answer.)

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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