Before calculating the exact x value with 72% of the values less than it, we are certain that x is _______.A. smaller than mean 3B. equal to mean 3C. Larger than mean 3 Assume a random variable X follows aN (3,5) distribution.1. What is the value of à such that72% of the values are less than it(72nd percentile)?2. What is the value of x such that47% of the values are greater thanit?3. Find the number 2* such that theproportion of z observationsbetween - z* and z* is 0.90.

The objective of the question is to find the value of x for a given percentile in a normal…

Answered: Assume a random variable X follows a N…

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

Before calculating the exact x value with 72% of the values less than it, we are certain that x is _______.

A. smaller than mean 3

B. equal to mean 3

C. Larger than mean 3

Assume a random variable X follows a
N (3,5) distribution.
1. What is the value of à such that
72% of the values are less than it
(72nd percentile)?
2. What is the value of x such that
47% of the values are greater than
it?
3. Find the number 2* such that the
proportion of z observations
between - z* and z* is 0.90.

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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