Question: A dust mite allergen level that exceeds 2 micrograms per gram (g/g) of dust has been associated with the development of allergies. Consider a random

A dust mite allergen level that exceeds 2 micrograms per gram (Âµg/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 2Âµg/g. The probability distribution for x, based on a study by the National Institute of Environmental Health Sciences, is shown in the following table:

a. Verify that the probabilities for x 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 2Âµg/g.
c. Find the probability that fewer than two homes in the sample have a dust mite level that exceeds 2Âµg/g.
d. Find E(x). Give a meaningful interpretation of the result.
e. Find Ïƒ.
f. Find the exact probability that x is in the interval Âµ Â± 2Ïƒ. Compare your answer with Chebyshev's rule and the empirical rule.

1 .30 2 .37 3 .20 p(x) .09 .04

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a Check whether the probabilities sum up to one Let x be the number of homes with dust mite level that exceeds 2 g g Therefore 009 030 037 020 004 1 T... View full answer

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