A company sells eggs in boxes with 12 cartons and 12 eggs in each carton, thus there are 144 eggs in each box.The organization wants to construct a P-chart to track the proportion of broken eggs in each sample (shown below).If the company used one box of eggs in each sample in the dataset below, what would be the centerline, upper control limit (UCL), and lower control limit (LCL) for the appropriate P-chart? (Use z = 3.) Choose the closest answer.
A) Centerline = 0.50, UCL = 0.625, LCL = 0.375
B) Centerline = 0.025, UCL = 0.64, LCL = 0
C) Centerline = 0.30, UCL = 0.70, LCL = 0
D) Centerline = 0.083, UCL = 0.152, LCL = 0.014

Question

A company sells eggs in boxes with 12 cartons and 12 eggs in each carton, thus there are 144 eggs in each box.The organization wants to construct a P-chart to track the proportion of broken eggs in each sample (shown below).If the company used one box of eggs in each sample in the dataset below, what would be the centerline, upper control limit (UCL), and lower control limit (LCL) for the appropriate P-chart? (Use z = 3.) Choose the closest answer. 
A) Centerline = 0.50, UCL = 0.625, LCL = 0.375 
B) Centerline = 0.025, UCL = 0.64, LCL = 0 
C) Centerline = 0.30, UCL = 0.70, LCL = 0 
D) Centerline = 0.083, UCL = 0.152, LCL = 0.014

Quizplus · Accepted Answer

The P-chart formula for the centerline, upper control limit (UCL), and lower control limit (LCL) is:
Centerline = P̂
UCL = P̂ + z * √(P̂(1-P̂)/n)
LCL = P̂ - z * √(P̂(1-P̂)/n)
where P̂ is the proportion of broken eggs, n is the sample size (which is 144 in this case), and z is the number of standard deviations from the mean (which is 3 in this case).

For the given data, the proportion of broken eggs is (11+8+10+12+9+13+7+14+8+11)/144 = 0.0868 or approximately 0.09.

Using the P-chart formula, we get:
Centerline = 0.09
UCL = 0.09 + 3 * √(0.09(1-0.09)/144) = 0.6398 or approximately 0.64
LCL = 0.09 - 3 * √(0.09(1-0.09)/144) = -0.018 or approximately 0 (set to 0 since proportion can't be negative)

Thus, the closest answer is B: Centerline = 0.025, UCL = 0.64, LCL = 0.

A Company Sells Eggs in Boxes with 12 Cartons and 12