(06.02) the table below shows data from a survey about the amount of time students spend doing homework each week. the students were either in college or in high school: high low q1 q3 iqr median mean σ college 50 5 7.5 15 7.5 11 13.8 6.4 high school 16 0 9.5 14.5 5 13 10.7 5.3 which of the choices below best describes how to measure the spread of this data? (hint: use the minimum and maximum values to check for outliers.) (2 points) select one: a. both spreads are best described with the iqr. b. both spreads are best described with the standard deviation. c. the college spread is best described by the iqr. the high school spread is best described by the standard deviation. d. the college spread is best described by the standard deviation. the high school spread is best described by

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.