For a statistics project a community college student at diablo valley college (dvc) decides to investigate cheating in two popular majors at dvc: business and nursing. she selects a random sample of nursing and business courses and convinces the professors to distribute a short anonymous survey in their classes. the question about cheating is one of many other questions about college life. when the student summarizes the data, she finds that 42 of the 50 business students and 38 of the 70 nursing students admitted to cheating in their courses. true or false? the counts suggest that the normal model is a good fit for the sampling distribution of sample differences

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.