4. (22 22) Medieval Nanotechmology IIl is considered the most challenging course

Question

4. (22 22) Medieval Nanotechmology IIl is considered the most challenging course at BU and the professor holds 10 quizzes during the semester. Liam is in the class and he judges his probability of passing any particular quiz to be about 0.6. (a) How many quizzes should Liam expect to pass? (b) What is the standard deviation of the number of quizzes he passes? (c) What is the probability that he passes exactly 5 quizzes? (d) What is the probability that he passes not more than 7 quizzes? (i) 0.2150 (ii) 0.1672 (iii) 0.6178 (iv) 0.8328

Explanation / Answer

a) E[X] = n*p = 10*0.6 = 6

b) V(X) = n*p*(1-p) = 10*0.6*0.4 = 2.4
Standard deviation = sqrt(2.4) = 1.54919

c) P(X = 5) = nCk * pk * (1-p)(n-k) = 10C5 * 0.65 * 0.45 = 0.2007

d) Using Normal approximation

P(X <= 7) = P(X < 7.5) = P(Z < (7.5-6)/1.549) = P(Z < 0.9684) = 0.8336

Answer: Option 4

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