fair dice? Problem 2 (8points) a) If the unemployment rate in Canada is 5%, what
ID: 3324773 • Letter: F
Question
fair dice? Problem 2 (8points) a) If the unemployment rate in Canada is 5%, what is the probability that a random sample of 10,000 will contain between 450 and 550 unemployed? An«I(#ulu.tr, ts; 'hiltrslix. itmi.v61bta:i on w.arsR ssstilisnbx3B:krti ili bliry 0.53), clay (probability 0.21), or sand. If it is a rock, a gcological test gives a positive result with 35% accuracy, if it is clay, this test gives a positive result with 45% accuracy, k) positive, what is the probability that the soil is rock?Explanation / Answer
Solution
1) Let X be the number of unemployed people in Canada
given p = 0.05 and n = 10000 so np = 500 and variance = npq = 500*0.95 = 475
P(450<X<550) = P((450-500)/(475)0.5<Z<(550-500)/4750.5)
P(-2.2942<Z<2.2942) = 2P(Z<2.2942)-1 = 0.9782
2) A : P(rock) = 0.53 , B : P(clay) = 0.21 and C : P(sand) = 0.26
Let D be the even that result is positive
P(D given A) = 0.35 , P(D given B) = 0.45 and P(D given C) = 0.75
P(A given D) = (0.53)(0.35)/((0.53)(0.35)+(0.21)(0.45)+(0.26)(0.75)) = 0.3905
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