Engineers want to design seats in commercial aircraft so that they are wide enough to fit 9090% of all males. (accommodating 100% of males would require very wide seats that would be much tooexpensive.) men have hip breadths that are normally distributed with a mean of 14.5 in. and a standard deviation of 1.2 in. find upper p90. that is, find the hip breadth for men that separates the smallest 90% from the largest 10%.

the hip breadth for men that separates the smallest 90% from the largest 10% is p90__in.

(round to one decimal place as needed.)

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.