Average monthly temperature month temperature january 45 degrees february 42 degrees march 54 degrees april 62 degrees may 78 degrees june 85 degrees july 92 degrees august 94 degrees september 89 degrees october 78 degrees november 65 degrees december 54 degrees the average monthly temperatures for the city of mathville are given in the chart above. one year, january's average temperature was 7 degrees warmer, february's was 3 degrees cooler, june's was 2 degrees cooler, august's was 3 degrees warmer, and november's was 7 degrees warmer. what did this do to the average yearly temperature? a) the average remained the same. b) the average increased by 1°. c) the average decreased by 1°. d) the average increased by 17°.

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.