p.803 - 20 - 2.39 (put the data in rank order)
22 - 2.28
24 - median
34 - There is so much variation, that it is not typical of any of the states.
p.814 - 30 - $80.38
32 - All of the values
41 - 18.29, 4.35
42 - 23.29, 4.35
45 - 54.86, 13.04
"For further thought" - 1 - positive if mean greater than median (skewed to right), negative if mean
less than medidian (skewed to left) [There is a definition of skewness which is
different from the skewness coefficient, but that need not concern us.]
2 - The magnitude of extreme values impacts the mean, but the median only depends on whether they are above or below the middle.
p.821 - 6 - 70
18 - I shall not draw a boxplots, but give the 5 number summaries: min: 10, Q1:
13, Q2(= median): 30.5, Q3: 69, max: 113; min: 6, Q1: 10, Q2(=median): 25, Q3: 37, max: 95
Note that by "position" the text means relative position.
23 - central tendency
25 - dispersion
26 - dispersion
32 - no (it will generally be less)
p.841 - 6 - 28% is not close to 50%; the point of this problem is that the smaller banknote is about 28% shorter than the larger banknote: do people perceive length or area?
12 - Assuming that the vertical axis is circulation and the horizontal is time,
it is clear that circulation has increased. But the axes should be labelled,
and we need the values to decide how significant the increase is (is the bottom
0?).
p.678 - 62 - 8 (list the numbers, the leading digit cannot be zero, there are 4 that end in 1 and 4 that end in 3) [201, 231, 301, 321, 103, 123, 203, 213]
p.689 - 38 - 5^5=3125 (anyone can work any day, counting with replacement.)
42 - 18 (3x3=9 end with 3 and 9 end with 5)
48 - 5^20 = (approx) 10^14
62 - 72 (3! ways to order the men times 3! ways to order the women, and you
can start with either a man or a woman (there are other ways to obtain this
answer such as their questions: a-6, b-3, c-2, d-2, e-1, f-1).
p.702 - 24 - C(24,5) = (24!)/((5!)(19!)) = 24x23x22x21x20/(5x4x3x2x1) =42504
34 - 4 x C(13,5) = 5148 (there are 4 suits)
60 - 1 (there is only one way to choose nothing - everything is discarded).
p.710 - 10 - C(7,2)xC(3,2) = 63 (2 democrats means 2 republicans)
p.709- "For Further Thought" - 3 - w^5 + 20w^4 + 160w^3 + 640w^4 + 1280w^5 + 1024 (the binomial coefficients are
multiplied by powers of 4)
5 - u^6 - 6(u^5)(v) + 15(u^4)(v^2) - 20(u^3)(v^3) + 15 (u^2)(v^4) - 6(u)(v^5) +v^6
p.731 - 8 - a)QHDH,QHDT,QTDH,QTDT (notation: coin (Q or D), outcome (H or T)),
b).5, c).5, d) 1/4, e) 2/4 = 1/2
12 - a) HHH, HHT, HTH, THH, HTT, THT, TTH, TTT; b)1/8, c) 3/8, d)3/8, e)1/8
46 - (C(13,2)C(11,1)C(4,2)C(4,2)C(4,1))/C(52/5) = .04753902 (I expect you to be
able to do this without the table)
49 - (C(13,5)-10)/C(52,5) = .00049135 (I expect you to be able to do this
without the table)
56 - 2x3!x3!/6! = .1 (eithe the womenor the men will begin the seating)
58 - 1/(5x4x3) = 1/60
p.742 - 4 - 2,3,4,5,6 are greater than or equal to 2, so 5/6 (or 1-P(less than 2) = 1- 1/6)
p.752 - 6 - not independent, the fraction of republicans remaining after one
senator is selected depends on whether the first selected was a republican)
30 - 1 (all queens are face cards) (4/4)
36 - You must also assume independence (which does not hold, but is
approximately true); with the birth order specified, (1/2)^3 = 1/8
52 - a) P(at least one face) = 1- P(no face); (40/52)(39/51)(38/50) ... (keep
going until the product is less than .5 (3 cards are needed); b)
(48/52)(47/51)(46/50)(45/49)(44/48)(43/47)(42/46)(41/45)(40/44)=.46, hence 9
cards
p.899 - 22 - 30x12x$1076.48 = $387532.80 24 - 387532.8 - 140000 = 247532.8 (interest); 247532.8-140000 = 107532.8 (excess of interest over principal)
July 2007