**Pollutant Distribution in Large Cities' Waterways**The pollutant levels in waterways near large cities follow a normal distribution with a mean (\(\mu\)) of 8.6 ppm (parts per million) and a standard deviation (\(\sigma\)) of 1.5 ppm. This study examines 39 randomly selected large cities. All results should be rounded to four decimal places.**Questions:**a. **Distribution of \( X \):** What is the distribution of \( X \)? \( X \sim N(\_\_\_\_, \_\_\_\_) \)b. **Distribution of \( \bar{x} \):** What is the distribution of sample mean \( \bar{x} \)? \( \bar{x} \sim N(\_\_\_\_, \_\_\_\_) \)c. **Probability for One City:** What is the probability that one randomly selected city's waterway will have pollutant levels less than 9.2 ppm? Probability: \_\_\_\_d. **Probability for 39 Cities:** For the 39 cities, find the probability that the average pollutant level is less than 9.2 ppm. Probability: \_\_\_\_e. **Normal Distribution Assumption:** Is the assumption that the distribution for part d) is normal necessary? Yes \[ \] No \[ \]f. **Interquartile Range (IQR) Calculation:** Calculate the IQR for the average pollutant level of the 39 cities. - \( Q1 = \_\_\_\_ \) ppm - \( Q3 = \_\_\_\_ \) ppm - IQR: \_\_\_\_ ppm The questions guide students to consider the properties of normal distributions and apply statistical methods to solve real-world problems related to environmental science.

Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you required unanswered sub parts also, kindly re-post those parts separately. Let X be the amount of pollutants that are found in waterways near large cities. From the given information, X follows normal distribution with mean µ=8.6 ppm and a standard deviation σ=1.5 ppm. a. Then, the distribution of X is normal.b. If X follows normal distribution with mean µ and a standard deviation σ, then x-bar follows normal distribution with mean µ and a standard deviation σ/(square root of n). Here, µ=8.6 The distribution of x-bar is normal.c. The probability that a randomly selected city’s waterway will have less than 9.2 ppm is Thus, the probability that a randomly selected city’s waterway will have less than 9.2 ppm is 0.6554.

Math

Statistics

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.6 ppm and standard deviation 1.5 ppm. 39 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 ? a - N( c. What is the probability that one randomly selected city's waterway will have less than 9.2 ppm pollutants? 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? f. Find the IQR for the average of 39 cities. Yes No Q1 ppm %3D Q3 ppm %3D IQR: ppm

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.6 ppm and standard deviation 1.5 ppm. 39 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 ? a - N( c. What is the probability that one randomly selected city's waterway will have less than 9.2 ppm pollutants? 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? f. Find the IQR for the average of 39 cities. Yes No Q1 ppm %3D Q3 ppm %3D IQR: ppm

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 25SGR

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