Exercise 4.2 gives the probability distribution for the number Y of homes with high dust mite levels.

a. Find E(Y). Give a meaningful interpretation of the result. 

b. Find s.

c. Find the exact probability that Y = y is in the interval μ ± 2σ. Compare to Chebyshev’s Rule and the Empirical Rule.

Data from Exercise 4.2

A dust mite allergen level that exceeds 2 micrograms per gram (mg/g) of dust has been associated with the development of allergies. Consider a random sample of four homes and let Y be the number of homes with a dust mite level that exceeds 2 mg/g. The probability distribution for Y  = y, based on a study by the National Institute of Environmental Health Sciences, is shown in the following table.

Transcribed Image Text:

y 2 4 p(y) .09 30 37 20 .04 3.