Use this information about 10 shipments of lightbulbs: If 200 lightbulbs are selected at random from each of 10 shipments and the number of defectives in each shipment is given above,find the LCL and the UCL for the p chart.
A)[0,.1044]
B)[.003,.017]
C)[0,.0311]
D)[.009,.0115]

Question

Use this information about 10 shipments of lightbulbs:  If 200 lightbulbs are selected at random from each of 10 shipments and the number of defectives in each shipment is given above,find the LCL and the UCL for the p chart.
A)[0,.1044] 
B)[.003,.017] 
C)[0,.0311] 
D)[.009,.0115]

Quizplus · Accepted Answer

The LCL and UCL for the p chart are calculated using the following formulas:
LCL = p̅ - 3√((p̅(1-p̅))/n)
UCL = p̅ + 3√((p̅(1-p̅))/n)
where p̅ is the overall proportion of defectives and n is the sample size (200 in this case).

To calculate p̅, we first need to find the total number of defectives across all shipments: 1+5+8+3+9+6+2+7+4+0 = 45. The total number of lightbulbs is 2000 (10 shipments x 200 lightbulbs per shipment). So, p̅ = 45/2000 = 0.0225.

Substituting p̅ and n into the formulas above, we get:
LCL = 0 - 3√((0(1-0))/200) = 0
UCL = 0.0225 + 3√((0.0225(1-0.0225))/200) = 0.0311

Therefore, the answer is C) [0, 0.0311].

Use This Information About 10 Shipments of Lightbulbs: If