Alumber company is making boards that are 2533.0 millimeters tall. if the boards are too long they must be trimmed, and if the boards are too short they cannot be used. a sample of 14 is made, and it is found that they have a mean of 2536.4 millimeters with a variance of 64.00. a level of significance of 0.05 will be used to determine if the boards are either too long or too short. assume the population distribution is approximately normal. is there sufficient evidence to support the claim that the boards are either too long or too short?

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.