p.650 - 20 - 2.39 (put the data in rank order)
22 - 2.28
24 - median
34 - 2,458,000 sq mi (2,458,400 rounded off)
36 - The problem is incoherent, if the countries are combined, the density is 264 persons per sq mi, the book gives 370, which is the mean among the population densities
p.659 - 30 - $80.38
32 - All of the values
41 - 18.71, 4.35
42 - 23.71, 4.35
45 - 56.14, 13.04
"For further thought" - 1 - positive if mean greater than median (skewed to right), negative if mean
less than median (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.665 - 2 - 70
18 - I shall not draw a boxplots, but give the 5 number summaries: min: 12, Q1:
29, Q2(= median): 54.5, Q3: 70, max: 261; min: 44, Q1: 51, Q2(=median): 78, Q3: 216, max: 339
22 - Measures of central tendency describe where the data set is, measures of (relative) position describe where a datum is within the data set
Note that by "position" the text means relative position.
23 - central tendency
25 - dispersion
26 - dispersion
32 - no
p.531 - 60 - 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.541 - 36 - 5^5 = 3125 (anyone can work any day, counting with replacement.)
40 - 3^3 = 27
p.541 - 4 - No, 6! = 720 does not equal (2!)(3!) = 12
p.553 - 24 - C(24,5) = (24!)/((5!)(19!)) = 24x23x22x21x20/(5x4x3x2x1) =42504
34 - 4 x C(13,5) = 5148 (there are 4 suits)
p.560 - 10 - C(7,2)xC(3,2) = 63 (2 democrats means 2 republicans)
"For Further Thought" - 3 - w^5 + 20w^4 + 160w^3 + 640w^2 + 1280w^1 + 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.585 - 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
56 - 2x3!x3!/6! = .1 (either the women or the men will begin the seating)
p.594 - 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.603 - 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)
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.587 - 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)
p.723 - 22 - 30x12x$1076.48 = $387532.80 24 - 387532.8 - 140000 = 247532.8 (interest); 247532.8-140000 = 107532.8 (excess of interest over principal)
August 2011