Answered: Students should spend average of 12…

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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Students should spend average of 12 hours studying. Survey done on 25 students and the distribution of total study hours per week is bell-shaped with a mean of 12 hours and a standard deviation of 2.7 hours

68% of students spend between ? hours and ? hours on stats each week

95% of students spend between ? hours and ? hours on stats each week.

99.7% of students spend between ? hours and ? hours on stats each week.

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 + ...

Expert Solution

Step 1

The provided information are:

Step 2

According to the empirical rule:

Approximately 68% of the data values fall within one standard deviation of mean.

Approximately 95% of the data values fall within two standard deviations of mean.

Approximately 99.7% of the data values fall within three standard deviations of mean.

Step 3

(a)

It is known that 68% of the data lies within one standard deviations of the mean.

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