The cheetah is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 miles per hour (mph) and is capable of speeds above 72 mph. The accompanying table contains a sample of the top speeds of 35 cheetahs. The sample mean and sample standard deviation of these speeds are 59.51 mph and 4.13 mph, respectively. A histogram of the speeds is bell-shaped. Complete parts (a) through (d) below. LOADING... Click the icon to view the top speeds of cheetahs. a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean? A. It is reasonable to apply the empirical rule. The data is quantitative and the histogram of the data is bell-shaped; therefore, the empirical rule applies. B. It is not reasonable to apply the empirical rule. The data is quantitative, but the value of k takes on values less than 1; therefore, the empirical rule is not appropriate. C. It is reasonable to apply the empirical rule. The data is quantitative and the mean and standard deviation are known; therefore, the empirical rule applies. D. It is not reasonable to apply the empirical rule. The data is quantitative and the histogram of the data is bell-shaped, but this does not imply that the data itself is bell-shaped; therefore, the empirical rule is not appropriate. b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean. Roughly nothing% of observations lie within one standard deviation to either side of the mean. Roughly nothing% of observations lie within two standard deviations to either side of the mean. Roughly nothing% of observations lie within three standard deviations to either side of the mean.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The cheetah is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 miles per hour (mph) and is capable of speeds above 72 mph. The accompanying table contains a sample of the top speeds of 35 cheetahs. The sample mean and sample standard deviation of these speeds are

59.51

mph and

4.13

mph, respectively. A histogram of the speeds is bell-shaped. Complete parts (a) through (d) below.

Click the icon to view the top speeds of cheetahs.

a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean?

It is reasonable to apply the empirical rule. The data is quantitative and the histogram of the data is bell-shaped; therefore, the empirical rule applies.

It is not reasonable to apply the empirical rule. The data is quantitative, but the value of k takes on values less than 1; therefore, the empirical rule is not appropriate.

It is reasonable to apply the empirical rule. The data is quantitative and the mean and standard deviation are known; therefore, the empirical rule applies.

It is not reasonable to apply the empirical rule. The data is quantitative and the histogram of the data is bell-shaped, but this does not imply that the data itself is bell-shaped; therefore, the empirical rule is not appropriate.

b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean.

Roughly

nothing%

of observations lie within one standard deviation to either side of the mean. Roughly

nothing%

of observations lie within two standard deviations to either side of the mean. Roughly

nothing%

of observations lie within three standard deviations to either side of 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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