CHAPTER 16. SECTION 16.1 (page 1168) SECTION 16.3 (page 1192) SECTION 16.2 (page 1179) Skills Review (page 1168) Skills Review (page 1192)

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1 Answers to Selected Eercises A CHAPTER SECTION. (page ) Skills Review (page )..,..,... nn n n. nn n. n!. n! Permutations of seating positions.,,.. (a) (b) (c). A: ; B: ; A.,.. (a), (b).....,.. nn n. n!.,.,.,,....,,... Because order matters, use permutations.. Because order does not matter, use combinations..,... P > C. Changing the order of an of the si elements selected results in a different permutation but the same combination.. Answers will var. SECTION. (page ). S ABC, ACB, BAC, BCA, CAB, CBA. S AB, AC, AD, AE, BC, BD, BE, CD, CE, DE (a) (b) (c). (a) (b) (c) (d).. (a) (b) (c). (a) (b) (c). (a) (b).. (a). (b).... (a) (b) (c). (a) (b) (c),...,,. Answers will var n!. No. n C r n P r n! but ma be greater than n P r r!. SECTION. (page ).. Skills Review (page )......%..%..%..%. Yes. No. No. Yes... Random variable Frequenc Random variable Frequenc Skills Review (page )....,...,,, P. P()..... S H, T, H, T, H, T, H, T, H, T, H, T The table represents a probabilit distribution.

2 A Answers to Selected Eercises. The table does not represent a probabilit distribution because the sum of the probabilities does not equal and P <.. P ). ) ) P ) f is not a probabilit densit function because e d e..... (a) (b) (a). (b)... E V.. f is not a probabilit densit function because d... f is a probabilit densit function. d f is a probabilit densit function..... d. f is a probabilit densit function. d. (a) (b) (c) (d) f is not a probabilit densit function because d and f < over the interval,. (a) (b) (c) (d)

3 Answers to Selected Eercises A. (a) (b). (c).. (a) e. (b) e. (c) e e. (d) (d)... (a) (b),,... % P() (a) (b) (a). (b).. E.. E. V. V... P() t. (a) S gggg, gggb, ggbg, gbgg, bggg, ggbb, (b) (c) P() gbgb, gbbg, bgbg, bbgg, bggb, gbbb, bgbb, bbgb, bbbg, bbbb (d). f is a probabilit densit function. sin d cos P. (a) E.; (b) $,. $. $.. Cit... (a) e. (b) e e. (c) e.. (a) e. (b) e e. (c) e.. (a) e. (b) e.... f is a probabilit densit function. d. (a) (b). (a) (b). (a). (b). SECTION. (page ) Skills Review (page )... ln. ln..... (a) (b). (a) (b) MID-CHAPTER QUIZ (page ).,.,,. (a) (b),

4 A Answers to Selected Eercises. (a) (b) (c). (a) (b) (c). (a) (b) (c).. : ln.. Uniform densit function : Variance: Standard deviation: t... Eponential densit function : Variance: Standard deviation:. Normal densit function : Variance: Standard deviation:. :. : Standard deviation: Standard deviation: P... : Standard deviation: P.. (a) About. (b) About. (c) About. (d) About.. (a) : : A.M. Standard deviation: (b). (a) ft et (b) e.. (a) ft et (b) e.. (a). standard deviations (b) About.%. (a). (b) (c) About... (a) (b) About. V. : median. : Median:.. : Median: ln.. ln. $... (a) Epected value: Standard deviation:. (b) About..,. P... minutes

5 Answers to Selected Eercises A. (a).% (b) No, about % of the emploees will be paid more than $./hr... (a) (b). (c). SECTION. (page ) Skills Review (page )... k... k. k k... k.,,,, First differences:,,, Second differences:,, Quadratic model: a n n n.,,,, First differences:,,, Second differences:,, Linear model: a n n.,,,, First differences:,,, Second differences:,, Neither linear nor quadratic. a. a n n n n n n. (a) First differences:,,, Second differences:,, (b) Quadratic model: d n n n (c) d n.n.n (d) Model from part (b) k.. k k k. Answers will var S n nn n. S n. S n n n. n : No, n : Yes, n : Yes, n : Yes. n : No, n : No, n : Yes, n : Yes. n : No, n : Yes, n : Yes, n : Yes. Answers will var.. Answers will var. See page.. Linear model: a n n. Quadratic model: a n n. Quadratic model: a n n.,,,, First differences:,,, Second differences:,, Linear model: a n n.,,,, First differences:,,, Second differences:,, Quadratic model: a n n n Model from part (c) Both models are good fits for the actual data. (e) No. For there to be an equal risk for each -mile-perhour increase in speed, the data would have to follow a linear pattern. SECTION. (page ) Skills Review (page ) z....

6 A Answers to Selected Eercises...., s s s s. s s s s s s..... The absolute values of corresponding numerical coefficients are the same. The terms of n alternate in sign... i.. t t t t t. z z z z...,,.!!!...., Fibonacci sequence. (a) gt.t.t (b). Answers will var. g f. (a) (b) (c)... S,,,.. n (a) (b). (a) (b) (c) (d). (a). (b) $,. V,.. V... n() P ). f is a probabilit densit function. ) d.. REVIEW EXERCISES FOR CHAPTER (page )... (a) (b) (c)..,.,,. (a), (b),,. S,,,,,,,,,.. (a) (b) (c). Although f is not a d, probabilit densit function because f < over the interval,.

7 Answers to Selected Eercises A. f is a probabilit densit function. d... (a) (b).... Variance: Standard deviation:. Variance: Standard deviation:.. ln.. (a) e e. (b) e e e e.. About... (a) (b). (c).... Answers will var.... S n n. Neither.,,,, n: a n : nd differences: st differences: Quadratic model: a n n n..... CHAPTER TEST (page ). (a) TTHH, TTHT, TTTH, TTTT; Random variable assigns numbers to each possible outcome, depending on the number of heads that turn up. (b) P. E ;.; P. E ; ; P >... V. P... V HTTH, HTTT, THHH, THHT, THTH, THTT, P.. Answers will var..... ANSWERS TO CHECKPOINTS SECTION....,.,,.....,. Permutations SECTION.. S AA, AB, AC, BA, BB, BC, CA, CB, CC...., S HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, Random variable, Frequenc of, n V.. P <. P.... (a) (b)..

8 A Answers to Selected Eercises SECTION unitsda. V.,. n() Probabilit P() Random variable SECTION.. P k S k k k. Answers will var.. Answers will var.. Answers will var... S k n. Quadratic model: a n n n. Linear model: a n n SECTION.. (a) (b). (a) (b).,,... (a) ab (b) ab.. d e d.... (a) About. (b) About. Because the graph of the probabilit densit function is smmetric about the line, ou know that the area under the graph over the interval, is equal to the area under the graph over the interval,. From Eample, ou know that the probabilit over, is about.. If ou subtract. from ou obtain.. Then divide. b to obtain approimatel., which is the probabilit from parts (a) and (b)... SECTION...,...%. :.; median:... About. or.%.. ;.