The Chair of the Quality Department at Motorola University wants to construct a p-chart for determining whether the four faculty members teaching the course are under control concerning the number of students who fail in the course.Accordingly,the Chair sampled 500 final grades from last year for each instructor,and computed the number of failures per instructor as 13,11,0,and 16 respectively.Compute the upper and lower standard control limits for this chart (rounded to 4 decimals).
A)0.9500 and 0.0500
B)0.0600 and 0.1400
C)0.0388 and 0.0012
D)0.1400 and 0.0000
E)None of the above

Question

Quizplus · Accepted Answer

First, we need to calculate the overall proportion of failures, which is the total number of failures divided by the total number of students:

(13 + 11 + 0 + 16) / (500 + 500 + 500 + 500) = 0.04

Next, we need to calculate the standard deviation of the sample proportions:

sqrt((0.04 * (1 - 0.04)) / 500) = 0.0388

Finally, we can calculate the control limits using the formula:

Upper control limit = overall proportion of failures + 3 * standard deviation of sample proportions
Lower control limit = overall proportion of failures - 3 * standard deviation of sample proportions

Upper control limit = 0.04 + 3 * 0.0388 = 0.1564 (rounded to 4 decimals)
Lower control limit = 0.04 - 3 * 0.0388 = 0.0012 (rounded to 4 decimals)

Therefore, the correct answer is C, with the upper control limit of 0.1564 and the lower control limit of 0.0012.

The Chair of the Quality Department at Motorola University Wants