The amount of pollutants that are found in waterways near large cities is normally distributed with mean 3.5 ppm and standard deviation 1.5 ppm. 15 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X-N( 8.5 1.5 b. What is the distribution of ? N(8.5 ✓ 0.3873 Or c. What is the probability that one randomly selected city's waterway will have less than 8.5 ppm pollutants? 0.5 d. For the 15 cities, find the probability that the average amount of pollutants is less than 8.5 ppm. e. For part d), is the assumption that the distribution is normal necessary? No Yes o f. Find the IQR for the average of 15 cities. Q1 = ppm Q3= ppm IQR: ppm
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 3.5 ppm and standard deviation 1.5 ppm. 15 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X-N( 8.5 1.5 b. What is the distribution of ? N(8.5 ✓ 0.3873 Or c. What is the probability that one randomly selected city's waterway will have less than 8.5 ppm pollutants? 0.5 d. For the 15 cities, find the probability that the average amount of pollutants is less than 8.5 ppm. e. For part d), is the assumption that the distribution is normal necessary? No Yes o f. Find the IQR for the average of 15 cities. Q1 = ppm Q3= ppm 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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![The amount of pollutants found in waterways near large cities is normally distributed with a mean of 8.5 ppm and a standard deviation of 1.5 ppm. 15 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
**a. What is the distribution of \(X\)?**
\[ X \sim N(8.5, 1.5) \]
**b. What is the distribution of \(\overline{x}\)?**
\[ \overline{x} \sim N(8.5, 0.3873) \]
**c. What is the probability that one randomly selected city's waterway will have less than 8.5 ppm pollutants?**
\[0.5\]
**d. For the 15 cities, find the probability that the average amount of pollutants is less than 8.5 ppm.**
**e. For part d), is the assumption that the distribution is normal necessary?**
\[ \text{Yes} \]
**f. Find the IQR for the average of 15 cities.**
- Q1 = _____ ppm
- Q3 = _____ ppm
- IQR = _____ ppm
Hints:
- [Hint](#)
- [Textbook Pages](#)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba867a91-7946-4dc8-8b92-57b0d80fa10e%2F7ee4b210-9cff-4a9c-8d46-89a20b769268%2Fsnzw6nl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The amount of pollutants found in waterways near large cities is normally distributed with a mean of 8.5 ppm and a standard deviation of 1.5 ppm. 15 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
**a. What is the distribution of \(X\)?**
\[ X \sim N(8.5, 1.5) \]
**b. What is the distribution of \(\overline{x}\)?**
\[ \overline{x} \sim N(8.5, 0.3873) \]
**c. What is the probability that one randomly selected city's waterway will have less than 8.5 ppm pollutants?**
\[0.5\]
**d. For the 15 cities, find the probability that the average amount of pollutants is less than 8.5 ppm.**
**e. For part d), is the assumption that the distribution is normal necessary?**
\[ \text{Yes} \]
**f. Find the IQR for the average of 15 cities.**
- Q1 = _____ ppm
- Q3 = _____ ppm
- IQR = _____ ppm
Hints:
- [Hint](#)
- [Textbook Pages](#)
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