You may have heard that bears cannot run very quickly downhill. According to many popular websites, this is a myth. To investigate, a wildlife researcher selects a random sample of 35 bears and gets them to individually run down a large hill by presenting a fish feast at the bottom of the hill. As they run he measures their speed in order to compute a confidence interval for the true mean downhill running speed for all bears. Are the conditions for calculating a confidence interval for μ met in this case? Explain.

Group of answer choices

Yes! Both the Random and Normal/Large Sample conditions are met.

We do not have enough information provided to determine if both of the conditions are met.

No. The Normal/Large Sample condition is met, but the Random condition is not met.

No. The Random condition is not met and the Normal/Large Sample condition is not met.

No. The Random condition is met, but the Normal/Large Sample condition is not met.

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.