In Denver Colorado the distribution of daily measures of amb

In Denver, Colorado, the distribution of daily measures of ambient nitric acid is skewed to the right; it has mean m = 1.81 micrograms per m³ and standard deviation s = 2.25 micrograms per m³.

Describe the sampling distribution of the mean ambient nitric acid of random samples of 40 Denverites. That is, specify the shape, the mean, and the standard error of the distribution.

What is the probability that a random sample of 40 Denverites will have a mean ambient nitric acid level smaller than 1.35 micrograms per m³?

Use the empirical rule to describe the range of mean ambient nitric acid levels of samples of 40 Denverites.

Solution

Here it is a sample of 40 Denverites, the sampling distribution of the mean ambient nitric acid of random samples of 40 Denverites will be at least approximately normally distributed with mean m = 1.81 and standard error = s/sqrt(n) = 2.25/sqrt(40) = 0.36. P(Mean < 1.35) = P(Z < (1.35 - 1.81)/0.36) = P(Z < -1.28) = 0.1003. More than 99% of the samples of 40 Denverites should have a mean ambient nitric acid level within 3 standard errors of the mean, that is between 1.81-3(0.36) = 0.73 and 1.81 + 3(0.36) = 2.89