w3t1 probability - 1.Determine whether each of the...

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1.   Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A)   No because the probability adds to 10/12 (B) Yes because the probability adds to 1 (0.2+0.4+0.4) (C) Yes because the probability adds to 1 (0.1+0.1+0.5+0.3) (Points :6) 2.   Consider a binomial distribution with 14 identical trials, and a probability of success of 0.6 i. Find the probability that x = 2 using the binomial tables ii. Use the normal approximation to find the probability that x = 2. Show all work. Consider a binomial distribution with 14 identical trials, and a probability of success of 0.6 i. Find the probability that x = 2 using the binomial tables I used a TI calculator to get P(x=2) = 14C2(0.6)^2(0.4)^12 = 0.00055.. =================================== ii.Use the normal approximation to find the probability that x = 2. Show all work. --- Find area over the interval (1.5,2,5) using u = np = 14*0.6 = 8.4, and std = sqrt(npq) = 1.833 ---- z(1.5) = (1.5-8.4)/1.833 = -3.7643 z(2.5) = (2.5-5.6)/1.833 = -3.2188 --- P(x=2) = P(-3.2188 < z < -3.7643) = 0.000560 x 1 2 3 4 P ( x ) 1/4 5/12 0.00 1/6 x 3 6 8 P ( x ) 0.2 2/5 0.4 x 20 35 40 50 P ( x ) 0.1 0.1 1/2 0.3
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 (Points :4) 3.   The diameters of oranges in a certain orchard are normally distributed with a mean of 7.10 inches and a standard deviation of 0.50 inches. Show all work. (A) What percentage of the oranges in this orchard have diameters less than 6.8 inches?
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