Answer:
3 sigma lower control limit = 0.0429
Explanation:
Given.
n = 100
days = 100
Number of defective bulbs = 600 defective bulbs
Let p = Process Average
p = 600/(100*40)
P = 600/4000
P = 0.15
q = 1 - p
q = 1 - 0.15
q = 0.85
3 sigma lower limit = p - 3*√(pq/n)
Using the above formula
Substitute in the values
3 sigma lower control limit = 0.15 - 3 * √(0.15 * 0.85/100)
3 sigma lower control limit= 0.15 - 3√0.001275
3 sigma lower control limit = 0.15 - 3* 0.035707142142714
3 sigma lower control limit = 0.15 - 0.107121426428142
3 sigma lower control limit = 0.04287857357185
3 sigma lower control limit = 0.0429 ---- approximated
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