Please give a detailed explanation, not just the answers. Thanks in advance!The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.3 ppm and standard deviation 1.3 ppm. 10 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. What is the probability that one randomly selected city's waterway will have more than 8.8 ppm pollutants? For the 10 cities, find the probability that the average amount of pollutants is more than 8.8 ppm. For part d), is the assumption that the distribution is normal necessary? No, YesFind the IQR for the average of 10 cities.Q1 = ppmQ3 = ppmIQR: ppm

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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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Please give a detailed explanation, not just the answers. Thanks in advance!

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.3 ppm and standard deviation 1.3 ppm. 10 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

What is the probability that one randomly selected city's waterway will have more than 8.8 ppm pollutants?
For the 10 cities, find the probability that the average amount of pollutants is more than 8.8 ppm.
For part d), is the assumption that the distribution is normal necessary? No, Yes
Find the IQR for the average of 10 cities.
Q1 =  ppm
Q3 =  ppm
IQR:  ppm

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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