Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given byx01234Px0.340.390.170.060.04 1. Find P(3)2. Find P(2 or fewer).3. Find the probability that the standard is exceeded on at least one day.4. Find the probability that the standard is exceeded on more than one day.5. Compute the mean ux. Round the answer to two decimal places.6.Compute the standard deviation σx. Round the answer to three decimal places.

The probability P(3) is given directly in the problem as 0.06.

Answered: Dirty air: The federal government has…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by

x	0	1	2	3	4
Px	0.34	0.39	0.17	0.06	0.04

1. Find P(3)

2. Find P(2 or fewer).

3. Find the probability that the standard is exceeded on at least one day.

4. Find the probability that the standard is exceeded on more than one day.

5. Compute the mean u_x. Round the answer to two decimal places.

6.Compute the standard deviation σ_x. Round the answer to three decimal places.

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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