Question

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.4 ppm and standard deviation 1.7 ppm. 40 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.What is the distribution of X ? X ~ N(,)What is the distribution of ¯x ? ¯x ~ N(,)What is the probability that one randomly selected city's waterway will have less than 9.1 ppm pollutants? For the 40 cities, find the probability that the average amount of pollutants is less than 9.1 ppm. For part d), is the assumption that the distribution is normal necessary? YesNoFind the IQR for the average of 40 cities.Q1 = ppmQ3 = ppmIQR: ppm

Answer 1

Given

mean = 9.4 ppm

standard deviation = 1.7 ppm

40 randomly selected large cities are studied.

Find

a) What is the distribution of X?

b) What is the distribution of ¯x?

c) What is the probability that one randomly selected city's waterway will have less than 9.1 ppm pollutants?

d) For the 40 cities, find the probability that the average amount of pollutants is less than 9.1 ppm.

e) For part d), is the assumption that the distribution is normal necessary?

f) Find the IQR for the average of 40 cities.

Q1 , Q3 , IQR:

Explanation

a) distribution of X = X ~ N(9.4 ,1.7)

b) distribution of ¯x

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{1.7}{\sqrt{40}}=0.26879360111\approx0.2688$

so , distribution of ¯x =

$\bar{x}(9.4,0.2688)$

c)