We showed that 19 minutes and 55 minutes (are/are) not 3 standard deviations from the mean. When we assume nothing about the shape of the distribution, we will use Chebyshev's Rule to get a sense of the distribution of data values. Chebyshev's Rule will tell usthe minimum percentage of observations that are within k standard deviations of the mean when k 2 1.100 1 -%We previously determined that 25 is two standard deviations below the mean and 49 is two standard deviations above the mean. Thus, we will use k =2 inChebyshev's Rule to determine the minimum percentage of times that are between 25 and 49 minutes.100 1- - 1% = 100 1-7575 %Thus, at least 7575 % of times are between 25 and 49 minutes.Step 4(c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 19 minutes or greater than55 minutes? (Round the answer to the nearest whole number.)Again, we are not assuming anything about the shape of the distribution, so we will continue using Chebyshev's Rule. We will determine the minimum percentage oftimes that are between 19 minutes and 55 minutes and then determine the maximum percentage of times that are less than 19 minutes or greater than 55 minutes.First, we need to know how many standard deviations 19 minutes and 55 minutes are from the mean so we can determine the value for k.We previously determined that 43 minutes and 31 minutes are 1 standard deviation from the mean and that 49 minutes and 25 minutes are 2 standard deviations fromthe mean.2531374349X-3sX-25X-5X+5X+ 25X+35Perhaps 19 minutes and 55 minutes are 3 standard deviations from the mean. Let's investigate.3 standard deviations above the meanx + 3s = 37 +:3 standard deviations below the mean3s - 37 - 3We showed that 19 minutes and 55 minutes-Select-- v3 standard deviations from the mean. Step 1(a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?To find the value that is some number of standard deviations above or below the mean, we will add or subtract some multiple of the standard deviation, s, to the samplemean, x. The average playing time was given to be 37 minutes with a standard deviation of 6 minutes, so we have x = 3737 and s = 6To find a value above the mean indicates we will use additionaddition . Finding a value below the mean indicates we will usesubtractionsubtraction. Finding values that are away from the mean includes values that are above and below the mean, indicating we will useaddition and subtractionaddition and subtractionStep 2We know the mean is x = 37 and the standard deviation is s = 6. To find values above the mean indicates addition, values below the mean indicates subtraction, and bothaddition and subtraction will be used to find values away from the mean.Find the value that is 1 standard deviation above the mean.1 standard deviation above the mean = x+s= 37 + 64343Find the value that is 1 standard deviation below the mean.1 standard deviation below the mean = x -s= 37 - 631Find the values that are 2 standard deviations away from the mean.2 standard deviations above the mean = x + 25= 37 + 2 66)49492 standard deviations below mean = x - 25= 37 - 262525

Answered: Image /qna-images/answer/4f130585-04c1-4c21-9f93-caa618423c88.jpg

Answered: (c) without assuming anything about the…

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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Question

100%

We showed that 19 minutes and 55 minutes (are/are) not 3 standard deviations from the mean.

When we assume nothing about the shape of the distribution, we will use Chebyshev's Rule to get a sense of the distribution of data values. Chebyshev's Rule will tell us
the minimum percentage of observations that are within k standard deviations of the mean when k 2 1.
100 1 -
%
We previously determined that 25 is two standard deviations below the mean and 49 is two standard deviations above the mean. Thus, we will use k =
2 in
Chebyshev's Rule to determine the minimum percentage of times that are between 25 and 49 minutes.
100 1- - 1% = 100 1-
75
75 %
Thus, at least 75
75 % of times are between 25 and 49 minutes.
Step 4
(c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 19 minutes or greater than
55 minutes? (Round the answer to the nearest whole number.)
Again, we are not assuming anything about the shape of the distribution, so we will continue using Chebyshev's Rule. We will determine the minimum percentage of
times that are between 19 minutes and 55 minutes and then determine the maximum percentage of times that are less than 19 minutes or greater than 55 minutes.
First, we need to know how many standard deviations 19 minutes and 55 minutes are from the mean so we can determine the value for k.
We previously determined that 43 minutes and 31 minutes are 1 standard deviation from the mean and that 49 minutes and 25 minutes are 2 standard deviations from
the mean.
25
31
37
43
49
X-3s
X-25
X-5
X+5
X+ 25
X+35
Perhaps 19 minutes and 55 minutes are 3 standard deviations from the mean. Let's investigate.
3 standard deviations above the mean
x + 3s = 37 +:
3 standard deviations below the mean
3s - 37 - 3
We showed that 19 minutes and 55 minutes-Select-- v3 standard deviations from the mean.

Step 1
(a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?
To find the value that is some number of standard deviations above or below the mean, we will add or subtract some multiple of the standard deviation, s, to the sample
mean, x. The average playing time was given to be 37 minutes with a standard deviation of 6 minutes, so we have x = 37
37 and s = 6
To find a value above the mean indicates we will use addition
addition . Finding a value below the mean indicates we will use
subtraction
subtraction. Finding values that are away from the mean includes values that are above and below the mean, indicating we will use
addition and subtraction
addition and subtraction
Step 2
We know the mean is x = 37 and the standard deviation is s = 6. To find values above the mean indicates addition, values below the mean indicates subtraction, and both
addition and subtraction will be used to find values away from the mean.
Find the value that is 1 standard deviation above the mean.
1 standard deviation above the mean = x+s
= 37 + 6
43
43
Find the value that is 1 standard deviation below the mean.
1 standard deviation below the mean = x -s
= 37 - 6
31
Find the values that are 2 standard deviations away from the mean.
2 standard deviations above the mean = x + 25
= 37 + 2 6
6)
49
49
2 standard deviations below mean = x - 25
= 37 - 26
25
25

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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