A professor has noticed that, even though attendance is not a component of the final grade for the class, students that attend regularly generally get better grades. In fact, 57% of those who come to class on a regular basis receive A's. Only 16% who do not attend regularly get A's. The long run attendance rate is 81%. Based on this class profile find the following:

Hint #1: pretend that there are 1000 students in the class and use the values given in the problem to construct the appropriate contingency table. Round cell frequencies to the nearest integer The first step to using hint #1 is to calculate the totals for those who attend regularly and do not attend regularly using the 'long run attendance rate'.

A) The percent who get A's given that they attend class regularly
B) The percent who get A's given that they do not attend class regularly
C) The overall percent of the students who get A's in the class
D) The percent who attend class regularly given that they get A's

.The total number of students in the class was given to be 1000 students. From the long run attendance rate (81%), the number of students that attend the class can be calculated;

The number of students that attend the class regularly = (81/100) *1000 = 810 students

While the number of the students who do not attend the class regularly = 1000-810 = 190 students

A. The number of students that get A’s because they attend regularly

= (57/100) *810 = 462 students (to the nearest integer)

So the percentage of students that get A’s given that they attend the class will be;

= (462/810) *100 = 57%

B. The number of students get A’s but they do not attend the class regularly;

= (16/100) *190 = 30 students (to the nearest integer)

Therefore, the percentage who get A’s given that they do not attend the class regularly is;

= (30/190) *100 = 16%

C. The total number of students who get A’s in the class = 462 +30 = 492 students

The percentage of the total number of students who get A’s in the class is;

= (492/1000) * 100 = 49.2%

D. Based on the fact that they get A’s, the percentage of people who attend the class will be;

= (462/492) *100 = 93.9%