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Mathematics, 21.02.2020 04:59 candiceforever123
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.
y 0 1 2 3 4
p(y) .09 .30 .37 .20 .04
(a) Find the probability that three or four of the homes in the sample have a dust mite level that exceeds 2 µg/g.
(b) Find the probability that fewer than three homes in the sample have a dust mite level that exceeds 2 µg/g.
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