Question 1 (a) American Heritage Investments headquartered in Boston, has a number of individuals clients who have recently opened 401(k) investment accounts. Each clients must to contribute on a monthly basis. The manager in charge 0140 1(k) investments at American Heritage Investments has collected a random sample of 100 clients who make monthly contribution to a 401(k). He has recorded the net dollars, after brokerage fees, which each client deposits into his or her account. He wishes to analyze the variation in these data by computing the range and the interquartile range. 33 164 173 184 190 197 207 216 224 237 53 164 175 186 191 197 207 217 225 240 150 164 175 186 191 198 208 217 225 240 152 166 175 186 192 200 208 217 229 240 157 166 178 187 193 200 208 219 231 250 I60 168 178 188 193 201 210 222 231 251 161 169 179 188 194 2m 21] 223 234 259 I62 171 180 188 194 204 212 223 234 270 162 17] 182 190 196 205 213 223 235 379 163 172 183 1.90 196 205 216 224 236 479 Compute: (i) Range [2marks] (ii) First and third quartiles [4marks] (iii) Interquartile range [4marks] (b) Consider a random variable, 2 that has a standardized normal distribution. Determine the following probabilities:- (i) P(O 1.645) [2marks] (iii) P(l.28 1) [2marks]