At the start of the semester,a professor wants to monitor students who miss class.The professor implements a new attendance policy geared toward encouraging students to attend class every day.There are currently 150 registered students in the class,and each day the class takes a quiz that is just used to measure attendance.The number of quizzes that are turned in will serve as the measure of attendance.The quizzes are given at every class period and the class meets four times per week over a 15-week semester.What is the value of the UCL?
A)Less than .5
B)Between .5 and .8
C)Greater than .8
D)None of the above

Question

Quizplus · Accepted Answer

The UCL (Upper Control Limit) is used in statistical process control to determine the upper limit of a process's key measurement before it is considered out of control. In this case, the process being monitored is attendance, and the key measurement is the number of quizzes turned in each day. The UCL can be calculated using the formula UCL = mean + 3sigma, where sigma is the standard deviation.

To calculate sigma, we need to know the average number of quizzes turned in each day and the variance in that number across the semester. Assuming that every student is present every day and turns in a quiz, the average number of quizzes turned in each day would be 150 (the total number of students). However, we cannot assume perfect attendance, so we need to estimate the average number of absent students per day and subtract that from the total number of students to get a more realistic estimate.

If we assume that 10% of students are absent every day, then the average number of quizzes turned in each day would be:

(0.9 x 150) = 135

To calculate the variance, we need to know how much the number of quizzes turned in varies from day to day. If we assume that attendance is random and independent across days, then we can use the formula for variance of a binomial distribution:

variance = n x p x (1 - p)

where n is the sample size (i.e., the number of students), and p is the probability of success (i.e., turning in a quiz) on any given day. If we assume that the probability of turning in a quiz is 0.9 (i.e., the complement of the assumed absence rate of 0.1), then the variance would be:

variance = 150 x 0.9 x 0.1 = 13.5

The standard deviation can be calculated by taking the square root of the variance:

sigma = sqrt(variance) = sqrt(13.5) = 3.68

Finally, we can calculate the UCL using the formula:

UCL = mean + 3sigma = 135 + 3(3.68) = 145.04

Since the number of quizzes turned in each day is an integer, we should round up to the nearest whole number:

UCL = 146

Therefore, the answer is C, Greater than 0.8.

At the Start of the Semester,a Professor Wants to Monitor