The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.2 ppm and standard deviation 1.7 ppm. 9 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of ? - N( c. What is the probability that one randomly selected city's waterway will have less than 8.3 ppm pollutants?
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.2 ppm and standard deviation 1.7 ppm. 9 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of ? - N( c. What is the probability that one randomly selected city's waterway will have less than 8.3 ppm pollutants?
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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![**Topic: Waterway Pollutant Distribution**
The amount of pollutants that are found in waterways near large cities is normally distributed with a mean of 9.2 ppm and a standard deviation of 1.7 ppm. A study is conducted focusing on 9 randomly selected large cities. The questions and tasks below analyze this data. Round all answers to four decimal places where possible.
a. **Distribution of \(X\):**
Determine the distribution of \(X\).
\[
X \sim N(\quad , \quad )
\]
b. **Distribution of \(\bar{x}\):**
Determine the distribution of \(\bar{x}\).
\[
\bar{x} \sim N(\quad , \quad )
\]
c. **Probability Calculation:**
What is the probability that one randomly selected city's waterway will have less than 8.3 ppm pollutants?
\[
\boxed{}
\]
d. **Probability for 9 Cities:**
For the 9 cities, find the probability that the average amount of pollutants is less than 8.3 ppm.
\[
\boxed{}
\]
e. **Normal Distribution Assumption:**
For part (d), is the assumption that the distribution is normal necessary?
\[
\text{No } \boxed{} \quad \text{Yes } \boxed{}
\]
f. **Interquartile Range (IQR):**
Find the IQR for the average of 9 cities.
\[
Q1 = \quad \text{ppm}
\]
\[
Q3 = \quad \text{ppm}
\]
\[
IQR = \quad \text{ppm}
\]
**Hint:**
To complete this set of questions, recall that you will need to use properties of the normal distribution, including standardizing the variable and potentially applying the Central Limit Theorem (CLT) when dealing with sample means.
This set of questions helps solidify the understanding of how normal distributions, sampling, and probability calculations relate to real-world data, such as pollutant levels in waterways.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3f191a8-a1b2-42ed-ac9e-32d60645d728%2Ff44d942b-c58b-439c-b507-0e3aa8b70a49%2F94gcpql_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Waterway Pollutant Distribution**
The amount of pollutants that are found in waterways near large cities is normally distributed with a mean of 9.2 ppm and a standard deviation of 1.7 ppm. A study is conducted focusing on 9 randomly selected large cities. The questions and tasks below analyze this data. Round all answers to four decimal places where possible.
a. **Distribution of \(X\):**
Determine the distribution of \(X\).
\[
X \sim N(\quad , \quad )
\]
b. **Distribution of \(\bar{x}\):**
Determine the distribution of \(\bar{x}\).
\[
\bar{x} \sim N(\quad , \quad )
\]
c. **Probability Calculation:**
What is the probability that one randomly selected city's waterway will have less than 8.3 ppm pollutants?
\[
\boxed{}
\]
d. **Probability for 9 Cities:**
For the 9 cities, find the probability that the average amount of pollutants is less than 8.3 ppm.
\[
\boxed{}
\]
e. **Normal Distribution Assumption:**
For part (d), is the assumption that the distribution is normal necessary?
\[
\text{No } \boxed{} \quad \text{Yes } \boxed{}
\]
f. **Interquartile Range (IQR):**
Find the IQR for the average of 9 cities.
\[
Q1 = \quad \text{ppm}
\]
\[
Q3 = \quad \text{ppm}
\]
\[
IQR = \quad \text{ppm}
\]
**Hint:**
To complete this set of questions, recall that you will need to use properties of the normal distribution, including standardizing the variable and potentially applying the Central Limit Theorem (CLT) when dealing with sample means.
This set of questions helps solidify the understanding of how normal distributions, sampling, and probability calculations relate to real-world data, such as pollutant levels in waterways.
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