Concentrations of a pollutant were measured at 25 locations in a lake after rains caused heavy runoff from surrounding areas. after a period of dry weather, they were measured again at the same locations. the data are in the file "runoff". find a 90% confidence interval for the effect of runoff on pollutant concentrations. 2. repeat problem 1 treating the rainy and dry measurements as independent samples. compare the results. which is the better procedure?

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.

The length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?

What’s a definition for a polygon inscribed in a sphere ?