The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 250.6 and a standard deviation of 69.5. (all units are 1000 cells/mul.) using the empirical rule, find each approximate percentage below. a. what is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 42.1 and 459.1? b. what is the approximate percentage of women with platelet counts between 111.6 and 389.6?

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.