1. A plastic bottle company is measuring the variation of the cap size that their newest machine produces. They gather the data from 1500 bottle caps and calculate the mean and standard deviation. The mean diameter of the bottle caps is 25 mm with a standard deviation of 1
mm.
Draw a Normal Distribution curve for this situation (1 point). For each question, show your work.

a. Of the 1500 bottle caps measured, how many bottle caps measured between 24 and 26 mm? (1 point)

b. Of the 1500 bottle caps measured, how many bottle caps measured 25 mm or less? (1 point)

C. Of the 1500 bottle caps measured, how many bottle caps measured between 22 and 28 mm? (1 point)

d. If you randomly choose 1 bottle cap and measure it, what is the likelihood that it will be between 23 and 27 mm?(1 point)

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.