Dust mite allergies. A dust mite allergen level that exceeds 2 micrograms per gram (µg/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 µg/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. y 1 2 3 4 PV) .09 30 .37 .20 .04 Dust mite allergies. Exercise 4.2 (p. 138) gives the proba- bility 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 o. c. Find the exact probability that Y = y is in the interval u ± 20. Compare to Chebyshev's Rule and the Empir- ical Rule.

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