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. 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.

1) Centerline = 0.50, UCL = 0.625, LCL = 0.375
2) Centerline = 0.025, UCL = 0.64, LCL = 0
3) Centerline = 0.30, UCL = 0.70, LCL = 0
4) Centerline = 0.083, UCL = 0.152, LCL = 0.014

Answer 1

To construct a P-chart to track the proportion of broken eggs in each sample, the centerline, upper control limit (UCL), and lower control limit (LCL) need to be calculated. The centerline is 0.083, the UCL is 0.152, and the LCL is 0.014.

Step-by-step explanation:

To construct a P-chart to track the proportion of broken eggs, we need to calculate the centerline, upper control limit (UCL), and lower control limit (LCL).

The centerline is calculated by dividing the number of broken eggs (12) by the total number of eggs (144). Therefore, the centerline is 12/144 = 0.083.

The standard deviation can be calculated using the formula sqrt(p(1-p)/n), where p is the proportion of broken eggs and n is the sample size. Since one box of eggs is used in each sample and there are 144 eggs in a box, the sample size is 144. To calculate the standard deviation, we need to calculate the proportion of broken eggs in each sample. In this case, it is 12/144 = 0.083. Plugging in the values, the standard deviation is sqrt(0.083(1-0.083)/144) ≈ 0.014.

The UCL is calculated by adding 3 times the standard deviation to the centerline, and the LCL is calculated by subtracting 3 times the standard deviation from the centerline. Therefore, the UCL is 0.083 + 3(0.014) ≈ 0.152 and the LCL is 0.083 - 3(0.014) ≈ 0.014.