Answered: he probability distribution of x, 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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he probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table.

x	0	1	2	3	4
p(x)	0.56	0.17	0.06	0.03	0.18

(a)

Calculate the mean value of x.

μ_x = tires per car

(b)

Interpret the mean value of x in the context of a long sequence of observations of number of defective tires.

In repeated inspections of cars at this station, the mean number of defective tires is tires per car.

(c)

What is the probability that x exceeds its mean value?

P(x > μ_x) =

(d)

Calculate the standard deviation of x. (Round your answer to four decimal places.)

σ_x = tires per car

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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