Question

QC.63 In preparation for their business launch, Heads Up embarked on a production blitz to produce a total of 350 custom headbands. It took Heads Up four days to produce these 350 headbands. In their rush, not all products were free of defects. After each day's production they sampled 35 units to determine the proportion of defective headbands. The table below contains the number of defective headbands for each sample on the four days: No. Defectives Sample Sample 1 Sample 2 Sample 3 Sample 4 | Based on the above information, what is their expected defect rate (proportion defective)? (Display your answer to four decimal places.) Number What is the standard deviation of the sampling distribution? (Display your answer to four decimal places.) Number What is the upper control limit for a 4-sigma control chart? (Display your answer to four decimal places.) Number What is the lower control limit for a 4-sigma control chart? (Display your answer to four decimal places.) Number

Answer 1

Answer: P bar = proportion defective= 0.0100

Answer b: standard deviation= 0.9900

Answer c: UCLp= 0.0605

Answer d: LCLp= 0.0000

Explanation:

sample	Defectives	Observations
Sample 1	2	35
Sample 2	1	35
Sample 3	2	35
Sample 4	3	35
total	8	140
steps and formulas, for z=3
Proportion of defects=Pbar	total defectives/total observations	0.0100
Q=	1-P	0.9900
N=	average sample size	35
Standard deviation	squareroot(P*Q/N)	0.0168
UCL=	P + z*squareroot(P*Q/N)	0.0605
LCL=	P - z*squareroot(P*Q/N)	-0.0405
	defects cannot be negative, therefore negative LCL is taken as '0'	0.0000