Question

2. The level of air pollutants in Los Angeles varies from day to day because of wind and weather. Overall though, some neighborhoods are very unhealthy. The level of PM2.5 (a type of small particles) in the Chinatown neighborhood of LA has an average of 160 μg/m³ (that’s micrograms per cubic meter). It varies day to day though, with a standard deviation of 22 μg/m³.

This last month has been particularly bad: for the last 31 days, the average has been 165 μg/m³. You want to know if that’s just random chance, or if the air pollution is getting worse.

a. Can we model the mean PM2.5 levels over 31 days using a Normal model? Check page 187 again, and answer in a complete sentence with why or why not.

b. Fill in this table.

Parameter	Mean	St.Dev.
x, daily PM2.5 levels
x̅, average PM2.5 for 31 days

c. What is the probability that x̅ would be over 165 for 31 days, just by random chance?

Answer 1

Answer Date: ---22/5/2019 a) Yes. According to CLT (Central Limit Theorem), the sample mean X is approximately normally distributed b) The table is given below. Parameter Mean St.Dev 160 165 c)The probability, 210 10) P(X 165 PZ> 22/V31 P (X > 165) = P(Z > 1.265401) P(X> 165)- $(-1.265401) P (X > 165) = 0.1029