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.If the company used one box of eggs in each sample in the dataset,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. $\begin{array}{|ll|ll|ll|}
\hline \text { Sample } & \text { Eggs } & \text { Sample } & \text { Eggs } & \text { Sample } & \text { Eggs } \
\hline 1 & 3 & 8 & 6 & 15 & 5 \
2 & 5 & 9 & 4 & 16 & 0 \
3 & 3 & 10 & 9 & 17 & 2 \
4 & 4 & 11 & 2 & 18 & 6 \
5 & 2 & 12 & 6 & 19 & 2 \
6 & 4 & 13 & 5 & 10 & 1 \
\hline 6 & 2 & 14 & 1 & \text { TOTAL } & 72 \
\hline
\end{array}$
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

Quizplus · Accepted Answer

The centerline (p-bar) is calculated as the total number of defects (72) divided by the total number of observations (1440, since there are 10 samples with 144 eggs each, not 20 as the table might misleadingly suggest due to a typo in the last sample number). This gives 72/1440 = 0.05. Using z=3 for the control limits, the formula for UCL is p-bar + z*(sqrt(p-bar*(1-p-bar)/n)), and for LCL it's p-bar - z*(sqrt(p-bar*(1-p-bar)/n)). Plugging in the numbers, we get UCL = 0.05 + 3*sqrt(0.05*0.95/144) ≈ 0.05 + 0.036 = 0.086, and LCL = 0.05 - 3*sqrt(0.05*0.95/144) ≈ 0.05 - 0.036 = 0.014, which doesn't match any option exactly due to a calculation mistake. The correct process, however, involves calculating the proportion of defects and applying the formula for UCL and LCL with the standard normal z-value. Given the options, B is the closest in terms of understanding the process, but the numbers provided in the answer choices do not accurately reflect the correct calculations based on the given data and standard formula for a P-chart. The correct calculation based on the provided data should yield a centerline of 0.05, but due to a mistake in my explanation, the exact UCL and LCL values provided do not match the correct formula outcome. The principle behind option B aligns most closely with the expected method for calculating a P-chart, despite the numerical inaccuracies in my response.

A Company Sells Eggs in Boxes with 12 Cartons and 12