Below is the probability distribution for the number x of homes with high dust mite levels. Number of Homes,

x 0 1 2 3 4 P(x) 0.09 0.30 0.37 0.20 0.04

x	0	1	2	3	4
P(x)	0.09	0.30	0.37	0.20	0.04

a) Find the expected value mean E(x).

b) Find the variance and standard deviation.

c) Find the interval of 2 and find the exactly probability that x falls in the interval. Compare your answer with the empirical rule and Chebyshev's rule.