PLEASE ANSWER ALL QUESTIONS, PLEASE DO NOT HAND WRITE ANSWERS AND PLEASE SHOW WO
ID: 3044131 • Letter: P
Question
PLEASE ANSWER ALL QUESTIONS, PLEASE DO NOT HAND WRITE ANSWERS AND PLEASE SHOW WORK, IF UNABLE TO, PLEASE LEAVE FOR SOMEONE WHO CAN, THANK YOU FOR YOUR ASSISTANCE
Quality Control?
Suppose that a company selects two people who work independently inspecting two-by-four timbers. Their job is to identify low-quality timbers. Suppose that the probability that an inspector does not identify a low-quality timber is 0.20.
What is the probability that both inspectors do not identify a low-quality timber?
How many inspectors should be hired to keep the probability of not identifying a low-quality timber below 1%?
Interpret the probability from part (a).
Explanation / Answer
from property of independence
probability that both inspectors do not identify a low-quality timber=P(first not identify)*P(second not identify)
=0.2*0.2 =0.04
let number of inspector required are x.
therefore probability that x inspector do not identify a low-quality timber =(0.2)x <0.01
taking log on both sides and solving:
x > ln(0.01)/ln(0.2)
x>2.86
x=3 =number of inspector required to keep the probability of not identifying a low-quality timber below 1%.
probability from part (a) reflect that on average 2 inspectors will not been able to identify 4 out of 100 low-quality timbers.
(please revert fr any clarification required)
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