Dust mite allergies. A dust mite allergen level that exceeds 2 micrograms per gr

Question

Dust mite allergies. A dust mite allergen level that exceeds 2 micrograms per gram (ug/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 g/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. 4.2 1 2 3 4 p(y) 09.30 .37 .20 04 a. Verify that the probabilities for Y in the table sum to 1. b. Find the probability that three or four of the homes in the sample have a dust mite level that exceeds 2 g/g. c. Find the probability that fewer than two homes in the sample have a dust mite level that exceeds 2 g/g.

Explanation / Answer

A) sum of of all probability = 0.09 + 0.3+ 0.37 + 0.2 + 0.04 = 1

B) P(X = 3 or 4) = P(X = 3) + P(X = 4) = 0.2 + 0.04 = 0.24

C) P(X < 2) = P(X = 0) + P(X = 1) = 0.09 + 0.3 = 0.39

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