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 in a state of 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.
A)0.9500 and 0.0500
B)0.0600 and 0.1400
C)0.0388 and 0.0012
D)None of the above

Question

Quizplus · Accepted Answer

To compute the upper and lower standard control limits for the p-chart, we need to use the following formula:
UCL = p̅ + 3√(p̅(1-p̅)/n)
LCL = p̅ - 3√(p̅(1-p̅)/n)
where p̅ is the average proportion of failures across all instructors, and n is the sample size (500 for each instructor).

To find p̅, we add up the number of failures for each instructor and divide by the total number of grades:
p̅ = (13+11+0+16)/(4*500) = 0.02

Substituting this value into the formula, we get:
UCL = 0.02 + 3√(0.02(1-0.02)/500) ≈ 0.0388
LCL = 0.02 - 3√(0.02(1-0.02)/500) ≈ 0.0012

Therefore, the correct answer is (C) 0.0388 and 0.0012.

The Chair of the Quality Department at Motorola University Wants