Answered: Suppose X is a random variable with…

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

Suppose X is a random variable with

X∼N(80,62)

and let

μ= the mean of X
me= the median of X
mo= the mode of X

a) Calculate the percentage of the data that is within 1.6 standard deviations of the mean. (2 decimal places)

b) The middle 50% of the data will be from ___ to ___ (2 decimal places)

c)Some of the descriptive statistics for the random variable

Z=X−80/6

are

the mean, μZ=
the standard deviation, σZ=
the 80th percentile of Z, P80=

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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