In recent years the Weibull distribution has been used to model engine emissions of various pollutants. Let X denote the amount of NOx emission (g/gal) from a randomly selected four-stroke engine of a certain type, and suppose that X has a Weibull distribution with α = 2 and β = 10 (suggested by information in the article “Quantification of Variability and Uncertainty in Lawn and Garden Equipment NOx and Total Hydrocarbon Emission Factors,” J. Air Waste Manag. Assoc. 2002: 435 – 448).
a. What is the cdf of X?
b. Compute P(X ≤ 10) and P(X ≥ 10).
c. Determine the mean and standard deviation of X.
d. Determine the 75th percentile of this distribution.