**Topic: Statistical Analysis of Pollutants in Waterways**The amount of pollutants found in waterways near large cities is normally distributed with a mean of 8.6 ppm (parts per million) and a standard deviation of 1.5 ppm. A sample of 39 randomly selected large cities is studied. Round all answers to four decimal places where possible.**Questions and Solutions:**a. **Distribution of X:** \(X \sim N(8.6, 1.5)\)b. **Distribution of \(\bar{x}\):** \(\bar{x} \sim N(8.6, 0.2402)\)c. **Probability of Less Than 9.2 ppm for One City:** The probability that one randomly selected city's waterway will have less than 9.2 ppm pollutants is 0.6554.d. **Probability for 39 Cities' Average Less Than 9.2 ppm:** (Blank space for answer, to be calculated)e. **Assumption of Normal Distribution:** Is the assumption that the distribution is normal necessary? - Answer: Nof. **Interquartile Range (IQR) for the Average of 39 Cities:** - \(Q1 =\) (Blank space for answer, to be calculated) ppm - \(Q3 =\) (Blank space for answer, to be calculated) ppm - IQR: (Blank space for answer, to be calculated) ppm**Instructions:**- Calculate any missing values using appropriate statistical formulas.- Understand the assumptions made for normal distribution in sample data.- Learn how to interpret the results of probability in a real-world context.

Note: Since up to part (c) are already answered, we will answer the remaining parts d,e,f. Given,…

The amount of pollutants that are found in waterways near large cities is normally distributed with m 8.6 ppm and standard deviation 1.5 ppm. 39 randomly selected large cities are studied. Round all ans to 4 decimal places where possible. a. What is the distribution of X? X - N( 8.6 V, 1.5 b. What is the distribution of æ? a - N( 8.6 0.2402 c. What is the probability that one randomly selected city's waterway will have less than 9.2 ppm pollutants? 0.6554 d. For the 39 cities, find the probability that the average amount of pollutants is less than 9.2 ppm. e. For part d), is the assumption that the distribution is normal necessary? O YesO No f. Find the IQR for the average of 39 cities. Q1 ppm %3D Q3 ppm %3D IQR: ppm

The amount of pollutants that are found in waterways near large cities is normally distributed with m 8.6 ppm and standard deviation 1.5 ppm. 39 randomly selected large cities are studied. Round all ans to 4 decimal places where possible. a. What is the distribution of X? X - N( 8.6 V, 1.5 b. What is the distribution of æ? a - N( 8.6 0.2402 c. What is the probability that one randomly selected city's waterway will have less than 9.2 ppm pollutants? 0.6554 d. For the 39 cities, find the probability that the average amount of pollutants is less than 9.2 ppm. e. For part d), is the assumption that the distribution is normal necessary? O YesO No f. Find the IQR for the average of 39 cities. Q1 ppm %3D Q3 ppm %3D IQR: ppm

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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