Answered: Refer to exercise 30 suppose that 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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Refer to exercise 30 suppose that the true mean file size of the music and video files on the tablet is 2.35 MB and you plan to take an SRS of n= 50 files.

Exercise 30: A tablet PC contains 3217 music files. The distribution of file size is highly skewed with many small file sizes. Assume that the stnadard deviaiton for this population is 3.25 megabytes (MB)

a) Explain why it may be reasonable to assume that the average x, with line on top of it (mean) is approximately normal even though the population distribution is highly skewed.

b) Sketch the appoximate normal curve for the sample mean, making sure to specify the mean and stanadard deviation.

c) What is the probability that your sample mean will differ from the population mean by more than 0.15 MB?

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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