A Pollen allergen level that exceeds 3 (micro grams per gram) of dust has been a
ID: 3208347 • Letter: A
Question
A Pollen allergen level that exceeds 3 (micro grams per gram) of dust has been associated with the development of allergies. Consider a random sample of four cars and let Y be the number of cars with a pollen level that exceeds 3 (micro grams per gram). The Probability distribution for Y=y ,is shown in the following table:
a-Verify that the probabilities for Y in the table sum to 1.
b-Find the probability that three or four of the cars in the sample have a pollen level that exceeds 3 (micro grams per gram).
c-Find the probability that fewer than two cars in the sample have a pollen level that exceeds 3 ( micro grams per gram).
y 0 1 2 3 4 p(y) .10 .40 .20 .05 .25Explanation / Answer
a. P(y)=0.10+0.40+0.20+0.05+0.25=1 so this is probability distribution
b. P(x=3)+P(x=4)=0.05+0.25=0.30
c. P(fewer than 2)=P(x=0)+P(x=1)=0.50