Ihave three errands to take care of in the administration building. let xi = the time that it takes for the ith errand (i = 1, 2, 3), and let x4 = the total time in minutes that i spend walking to and from the building and between each errand. suppose the xi's are independent, and normally distributed, with the following means and standard deviations: μ1 = 13, σ1 = 4, μ2 = 5, σ2 = 1, μ3 = 8, σ3 = 2, μ4 = 14, σ4 = 5. i plan to leave my office at precisely 10: 00 a. m. and wish to post a note on my door that reads, "i will return by t a. m." how long should i estimate my trip will take if i want the probability of the trip taking longer than my estimate to be 0.01? (round your answer to two decimal places.)

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.