(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 this is geometric distribution with paramter p=0.30

b) P(survey only one or two residents) =P(first have adequate supplies)+P(first not and second have adequate supplies) =0.3+(1-0.3)*0.3=0.51

c )

P(must survvey at least 3) =P(till first 2 residents none have adequate supplies)=(1-0.3)2 =0.49

d)

expected value =1/p=1/0.3=3.33

V X =(1-p)/p2 =(1-0.3)/0.32 =7.7778

SD X =(7.7778)1/2 =2.7889

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