The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.9 ppm and standard deviation 1.6 ppm. 14 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.What is the distribution of XX? XX ~ N(,)What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)What is the probability that one randomly selected city's waterway will have more than 10.1 ppm pollutants? For the 14 cities, find the probability that the average amount of pollutants is more than 10.1 ppm. For part d), is the assumption that the distribution is normal necessary? NoYesFind the IQR for the average of 14 cities.Q1 = ______ppmQ3 = ______ppmIQR: ______ppm

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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 7E

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The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.9 ppm and standard deviation 1.6 ppm. 14 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the probability that one randomly selected city's waterway will have more than 10.1 ppm pollutants?
For the 14 cities, find the probability that the average amount of pollutants is more than 10.1 ppm.
For part d), is the assumption that the distribution is normal necessary? NoYes
Find the IQR for the average of 14 cities.
Q1 = ______ppm
Q3 = ______ppm
IQR: ______ppm

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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