Answers 1 a z 83 706217 b z 66 706 067 c 9525 d 15 e 9082 f 7996 1666 996 70

# Answers 1 a z 83 706217 b z 66 706 067 c 9525 d 15 e

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Answers 1. a. z = (83-70)/6=2.17 b. z = (66-70)/6 = -0.67 c. 95.25% d. 1.5% e. 90.82% f. 79.96 ... 1.66*6 = 9.96 .... 70 + 9.96 = 79.96 g. 56.98...-2.17 * 6 = -13.02 .... 70 - 13.02 = 56.98 h. This observation is 1.64 sd above the mean, which is 1.64 * 6 = 9.84 points, so the score is 79.84 points. i. This observation is 0.77 sd below the mean. (Note 22%ile rank means that 28 % of the observations are between this score and the mean, so you look up .2800 in the body of the table.) So 0.77 * 6 = 4.62 points below the mean. The score is 70 – 4.62 = 65.48 j. The score 60 and 80 are both, conveniently, 10 points below the mean, making this a symmetric problem. You can find the area 10 points above and multiply by 2. The z score for 10 points above the mean is 10/6 = 1.67, which includes 45.25 % of cases. So the total is 45.25% * 2 = 90.5% k. The most extreme 20 percent of cases would be the 10 percent at the bottom end and the 10 percent at the top end, again making this a symmetric problem. The cutoff for the10% tail includes the 40% area, so the associated z score for the value of .4000 is 1.28. Converting this z score to a real score gives us 7.68 units above and below the mean. So the cutoffs are 70 - 7.68 = 62.32 and 77.68.
2. Area from 45 to 52 Z = (45-52)/ - 8.3 = - 0.84 ... This transforms to 29.95% Area from 52 to 55 Z = (55-52)/8.3 = 0.36 ... This transforms to 14.06% Together, this means 44.01 percent of House districts were competitive. 3. a. Z = (3.5 – 3.2)/1.1 = 0.3/1.1 = 0.27 b . Using table, proportion above z + 0.27 is 0.3936. So 1.000 – 0.3936 = 0.6064. So, with rounding, percentile rank is 60.6% c. z = (2.1 – 3.2)/1.1 = -1.1/1.1 = -1.0
4. a. Z = (700 – 650)/88 = 50/88 = 0.57 Using table, the percentage above this Z is 28.43 % b. Z score for 600 is same as Z score for 700, but negative. Thus, we know from part a of this problem that 28.43% lies outside of (below) 600 and 28.43 % lies outside of (above) 700, for a total of 56.86 percent outside these two points. Thus, 100% - 56.86% = 43.14% is the answer. c. Use table to find a number in the body of the table close to 25% or 0.2500. Closest is 0.2514, corresponding to a Z score of -0.67. Plug this into Z formula -0.67 = (x – 650)/88 . Solving for x, we get 591.

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