A dust mite allergen level that exceeds 2 micrograms per gram (mu g/g) of dust h

Question

A dust mite allergen level that exceeds 2 micrograms per gram (mu g/g) of dust has been associated with the development of allergies. Consider a random sample of four homes, and let x be the number of homes with a dust mite level that exceeds 2 mu g/g. The probability distribution for x, based on a certain study, is shown in the following table. Complete parts a through c. a. Find the sum of all probabilities for x in the table. b. Find the probability that three or four of the homes in the sample have a dust mite level that exceeds 2 mu g/g. The probability is c. Find the probability that fewer than two homes in the sample have a dust mite level that exceeds 2 mu g/g. The probability is

Explanation / Answer

a. the sumof all the probabilites are 0.13+0.34+0.24+0.25+0.04 = 1

b. P(X=3)+P(X=4) = 0.25+0.04 = 0.29

c. P(X=0)+P(X=1) == 0.13+0.34 = 0.47

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