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.

(a) 0.24

(b) 0.76

Step-by-step explanation:

We are given that let Y be the number of homes with a dust mite level that exceeds 2 mg/g. The probability distribution for Y=y is shown below ;

     y                 P(y)

     0                 0.09

     1                  0.30

     2                 0.37

     3                 0.20

    4                  0.04

(a) Probability that three or four of the homes in the sample have a dust mite level that exceeds 2 µg/g = P(y = 3) + P(y = 4)

                                           = 0.20 + 0.04 = 0.24 .

(b) Probability that fewer than three homes in the sample have a dust mite level that exceeds 2 µg/g = P(y = 0) + P(y = 1) + P(y = 2)

                                           = 0.09 + 0.30 + 0.37 = 0.76 .

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.  

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."