An experiment is conducted to select a suitable catalyst for the commercial prod

Question

An experiment is conducted to select a suitable catalyst for the commercial production of ethylenediamine (EDA), a product used in soaps. Suppose a chemical engineer randomly selects 3 catalysts for testing from a group of 10 catalysts, 6 of which have low acidity and 4 of which have high acidity. Find the probability that no highly acidic catalyst is selected. Find the probability that exactly one highly-acidic catalyst is selected. How many highly acidic acids would you expect to be chosen? What is the standard deviation of the number of highly acidic catalysts chosen?

Explanation / Answer

(a) N = 10, k = 4, n = 3

P(x) = C(k, x) C(N – k, n – x) / C(N, n)

P(0) = C(4, 0) C(10 – 4, 3 – 0) / C(10, 3) = 0.1667

(b) P(1) = C(4, 1) C(10 – 4, 3 – 1) / C(10, 3) = 0.5

(c) Mean = nk/N = 3 * 4/10 = 1.2

(d) Variance = (nk/N)(N – k)(N – n) / N(N – 1) = (3 * 4/10)(10 – 4)(10 – 3) / 10(10 – 1) = 0.56

Standard deviation = 0.56 = 0.7483

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