(8) It has been estimated that only about 30% of California residents have adequ

Question

(8) It has been estimated that only about 30% of California residents have adequate earthquake supplies Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies (a) What is this distribution? What are its parameter(s)? (b) What is the probability that we must survey just one or two residents until we find a California resident who does have adequate earthquake supplies? California resident who does have adequate earthquake supplies? California resident who does have adequate earthquake supplies? Also calculate VX and SDX (c) What is the probability that we must survey at least three California residents until we find a (d) On average, how many California residents do you expect to need to survey ul you find a

Explanation / Answer

a)

here number of residents surveyed till we fund a resident to have adequate earthquake supplies follows geometric distribution with paramter p=0.30

b)

P(one or two residents to be surveyed)=P(first one success)+P(first one failure and second success)

=0.3+0.7*0.3=0.51

c)

P(at least 3 to be surveyed)=P(first 2 are failures)=(1-0.3)2 =0.49

d)

expected to be surveyed =1/p=1/0.3 =3.33

V X =(1-p)/p2 =7.7778

SD X =(7.7778)1/2 =2.7889

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