The number of hits to a website follows a Poisson process. Hits occur at the rate of 0.4 per minute between 7:00 P. M. and 10:00 P. M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 8 : 27 P. M. and 8:31 P. M. Interpret each result. (a) exactly seven (b) fewer than seven (c) at least seven

15 points! write the slope-intercept form of the equation of the line through the given point with the given slope. use y-y = m(x-x) to solve. through (2,5) slope= undefined

Akitchen is 12 ft. by 14 ft. with 10 ft. high walls. how much would it cost to put vinyl flooring in this room? $8.80 per ft

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.