Data collected over a long period of time show that the length of time x to complete a particular college entrance test is normally distributed with an average of 125 minutes and a standard deviation of 18 minutes. ordinarily entrance tests have a time limit. what maximum time limit should be set for this entrance test if it is desired to have no more than 8% of test takers fail to finish the test during that time limit? round your answer to the nearest minute. don't forget that we round all z values to two decimal places. to answer the question input only the actual whole number. do not include units. do not give your answer in sentence form -- just include the numerical answer.

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.