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STATISTICS 200 MIDTERM EXAM-KIM,MOSE

# STATISTICS 200 MIDTERM EXAM-KIM,MOSE - STATISTICS 200...

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STATISTICS 200 MIDTERM EXAM NAME: Kim, Mo Se 1. This is an open book exam. 2. Plan to spend one hour to complete it. 3. Submit your completed exam into the assignment folder MT (midterm) 1. Calculate the probability of having 14 girls in 14 children. Write your formulae neatly to show ALL the steps and place the answer in scientific notation. (10 points) G = A girl P(G) = 1/2 = 0.5 P(all 12 girls) = P(G1 and G2 and G3 and ……. G13 and G14) = P(G1) x P(G2) x P(G3) …… x P(G13) x P(G14) = (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) = (0.5)^14 = 0.00006103515625 In Scientific notation this is 6.103515625 x 10^-5 2. Solve the permutation and combination using the formulas supplied. (10 points) Formulas 3!= (3)(2)(1) ! ( )! n r n P n r = - ! ( )! ! n r n C n r r = - 25 P 4 25!/(25-4)! = 25!/21! = (25)(24)(23)(22) = 303600 53 C 2 (53)!/{(53-2)!2!} = 53!/{(2)!(5!)} = {(53)(52)} / {(2)(1)} = 2756 / 2 = 1378 3. Determine the probabilities of blood groups using the chart below. Show all your work. (15 points) Group O A B AB TOTALS Rh class Rh+ 39 35 8 4 86 Rh class Rh- 6 5 2 1 14 Totals 45 40 10 5 100 P(Rh-) P(Rh-) =14/100 = 0.14 P(A) P(A)=40/100 = 0.4 P(Rh+) P(Rh+)=86/100 = 0.86 P(A and Rh+) P(A and Rh+) = (From the chart) 35/100 = 0.35 P(A or Rh+) P(A) + P(Rh+) – P(A and Rh+) = 0.40 + 0.86 – 0.35 = 0.91 4. Find the age of the actress in the chart on page 130 of your text using the percentile given and the locator formula L = (k/100) x n, where n = 76 (5 points) Percentile Calculation for the position of the actress in the chart Age P 10 L = (10/100)76 = 7.6 8 th 25 P 66 L= (66/100)76 = 50.16 51th 37 P 75 L= (75/100)76 = 57 (39+40)/2 = 39.5

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