1. (a) C. (b) 77. 5 (c) A - . (d) 31/5. (e) 25x8y10. (f) 3. (g) y = 1x + 1 2. It is reasonable to assume that more fighters are sent to bigger fires since bigger fires would typically be more difficult to bring under control. Bigger fires cause more widespread damage and would therefore often result in a larger damage bill. Therefore it is the size of the fire and not the number of firemen that cause an increase in damages. 3. (a) +($68, 000 + $32, 000 + $47, 000 + $50, 000 + $46, 500 + $19, 000 + $39, 500) = $43, 142.86. (b) In increasing order the values are $19,000 $32,000 $39, 500 $46, 500 $47, 000 $50, 000 $68, 000. There is an odd number of values so the median is the (7+1)/2 = 4th order value which is $46,500. (c) i. C. ii. B. 4. (a) See below: Histogram A 61.5 Histogram B 74.9 Histogram C 51.0 Histogram D 96.4 (b) See below: Histogram A 5.0 Histogram B 39.2 Histogram C 12.3 Histogram D 23.0 5. See below: 6. (a) 2 × 6 = 12. Correlation =0.05 -0.85 Correlation = 0.9 Correlation = 0.99 ?ª Correlation = - 0.6 Correlation = 0.6 (b) 1/12. (c) Possible outcomes are (T, 1) and (T,2). So P(A) = 2/12 = 1/6. (d) 1 - 1/6 = 5/6.
(e) If (T, 1) occurs then both A and B occur. So A and B are not mutually exclusive. (f) There are more simple events that comprise B (3 total) so B is more likely. 7. (a) P(H1) = 10/47. (b) P(H2|H1) = 9/46. (c) P(H1 and H2) = 19 x 2 46 45 (d) 1 - 45/1081 = 1036/1081. 1081. 8. (a) 18/37. (b) (18/37)5 ~ 0.027. (c) 18/37 since the wheel does not remember what happened previously. (d) Because the probability of five spins in a row landing on red is small at 0.027, the gambler believes that the probability of the ball landing on red on the next spin is also 0.027. But, as pointed out above, the wheel can't adjust its behavior based on past events so that the next spin has probability 18/37 still of landing on red. The gambler is a victim of the gambler's fallacy. 9. (a) p= 0.25. (b) 0,1, ... , 30. (c) 0.25 x 30 = 7.5. (d) 12/30 = 2/5 (e) 0.4+ 1.96x (0.4× 0.6)/30 which gives (0.225, 0.575) when rounded to three decimal places. (f) No since 0.25 is in the confidence interval for p. 10. (a) See below: 3 1 11- 3a 3 1=1 3 >(r2 - a2) 1=1 3 >(T1 - a) 1=1 3 X(z-a)2 1=1 3 1 3 >(T1 - a) 1=1 3 Er2-a2 1=1 ?-3a (I1 -a)2 + (12 -a)2 + (13 -a)2 2} + 1} + r} - a2 (1} + 12 + r}) - 3a2 I-a 3(T-a) (b) F. (c) D. (d) D. (e) C. (f) D. Reasoning: The