Five in every 100 slaughtered chickens passes inspection with fecal contaminatio

Question

Five in every 100 slaughtered chickens passes inspection with fecal contamination. Consider a random sample of three slaughtered chickens that all pass inspection. Let x equal the number of chickens in the sample that have fecal contamination. Complete parts a through c below. Find p(x) for x = 0, 1, 2, and 3. p(0) = __________ Calculate p(x) for x = 1. p(1) = ___________ Calculate p(x) for x = 2. p(2) = ______________ Calculate p(x) for x = 3. p(3) = ____________ Graph p (x). Choose the correct graph below. A. B. C. D. Find P(x lessthanorequalto 1) P(x lessthanorequalto 1) = __________ The chance of winning a lottery game is 1 in approximately 21 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $7 million grand prize. Calculate your expected net winnings for this single ticket. Interpret the result. Find mu = E(x). mu = __________ Interpret the result. Choose the correct answer below. Your average (1) _________ for a large number of games would be $ ________ per game winnings losses

Explanation / Answer

As multiple questions are posted, only the first one will be answered.

4. Proportion of passing = 5/100 = 0.05

Number of chickens passing follows a binomial distribution with n=3 and p=0.05

a. P(0) = 3C0 * (0.05)0 (1-0.05)3-0 = 0.857375

P(0) = 3C1 * (0.05)1 (1-0.05)3-1 = 0.135375

P(0) = 3C2 * (0.05)2 (1-0.05)3-2 = 0.007125

P(0) = 3C3 * (0.05)3 (1-0.05)3-3 = 0.000125

b. Graph of p(x):

Answer: B.

c. P(X <= 1) = p(0) + p(1) = 0.857375 + 0.135375 = 0.992750

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