wpp2.ms (2055B)
1 .TL 2 Weekly past paper 2 (stats) 3 .AU 4 Lucas Standen 5 .AI 6 QMC 7 8 .AB 9 .CD 10 .I 11 I thought for all our sanities, we might appreciate me trying to type this :) 12 .AE 13 14 .PP 15 1)a) 16 .EQ 17 22 - 16 over sigma = 1.28155 18 .EN 19 20 .EQ 21 sigma = 22 - 16 over 1.28155 22 .EN 23 24 .EQ 25 sigma = 4.68 26 .EN 27 28 .PP 29 1)b) 30 31 .EQ 32 P(L < 16) = P(Z < 13-16 over 4.68 ) 33 .EN 34 35 .EQ 36 P(L < 16) = 26.1% 37 .EN 38 39 .PP 40 1)c) 41 42 .EQ 43 P(S < 8) = 0.1 44 .EN 45 46 .EQ 47 {8 - mu} over sigma = -1.2816 48 .EN 49 50 .EQ 51 {17 - mu} over sigma = 0.8416 52 .EN 53 54 .EQ 55 sigma = 4.238 56 .EN 57 58 .EQ 59 mu = 13.432 60 .EN 61 62 .PP 63 1)d) 64 .EQ 65 13.4 > 16 66 .EN 67 68 .EQ 69 "this supports thier belief" 70 .EN 71 72 .PP 73 2)a) 74 75 .EQ 76 W = " The number of cards out of the 20 winning ones" 77 .EN 78 79 .EQ 80 W " ~ " B(20, 0.45) 81 .EN 82 83 .EQ 84 S = " The number of stores with 12 or more winning cards" 85 .EN 86 87 .EQ 88 S " ~ " B(8, p) 89 .EN 90 91 .EQ 92 p = P(w >= 12) = 0.1308 93 .EN 94 95 .EQ 96 P(S >= 2) = 0.2818 97 .EN 98 99 .PP 100 2)b) 101 102 .EQ 103 "There is a large number of trials, so the rate should be close 0.5" 104 .EN 105 106 .PP 107 2)c) 108 .EQ 109 X " ~ " N(135, 74.25) 110 .EN 111 112 .EQ 113 P(X < 122.5) 114 .EN 115 116 .EQ 117 P(Z < {122.5 - 135} over sqrt 74.25 ) = 0.0734 118 .EN 119 120 .PP 121 2)d) 122 .EQ 123 "The probability is higher than 2.5% therefore there is not enough evidence to suggest that the proportion is not 45%" 124 .EN 125 126 .PP 127 3)a)i) 128 .EQ 129 X " ~ " N(30, 2 sup 2 ) 130 .EN 131 132 .EQ 133 P(X = 31) = 0 134 .EN 135 136 .PP 137 3)a)ii) 138 .EQ 139 P(X > 31) = 0.3085 140 .EN 141 142 .PP 143 3)b)i) 144 .EQ 145 0.0668 times (1 - 0.0668) sup 4 = 0.0507 146 .EN 147 148 .PP 149 3)b)ii) 150 .EQ 151 P(Y > 1) = 1 - P(Y <= 1) 152 .EN 153 154 .EQ 155 1 - 0.9610 = 0.039 156 .EN 157 158 .PP 159 3)c) 160 .EQ 161 H " ~ " N( mu , 1.5 sup 2 ) 162 .EN 163 164 .EQ 165 P(H > 42) = 0.0005 166 .EN 167 168 .EQ 169 z = {42 - mu} over 1.5 = 3.29 170 .EN 171 172 .EQ 173 mu = 37.06 174 .EN 175 176 .PP 177 4)a) 178 .EQ 179 "mean "= 1680 over 60 = 28 " mins " 180 .EN 181 182 .EQ 183 S sub xx = 47654.4 - 1680 sup 2 over 60 = 614.4 184 .EN 185 186 .EQ 187 sigma = sqrt {S sub xx over 60} = 3.2 188 .EN 189 190 .PP 191 4)b) 192 .EQ 193 H sub 0 : mu = 27.5 194 .EN 195 196 .EQ 197 H sub 1 : mu > 27.5 198 .EN 199 200 .EQ 201 z = 28 - 27.5 over {3 over sqrt 60} = 1.2909 202 .EN 203 204 .EQ 205 z = 1.64485 206 .EN 207 208 .EQ 209 "no sufficent evidence to support her belief" 210 .EN 211 212 .PP 213 4)c)i) 214 .EQ 215 "assuming that you will always have a p of 0.2 is not likely" 216 .EN 217 218 .PP 219 4)c)ii) 220 .EQ 221 "moddel the fastest and slowest people as 2 distributions" 222 .EN