the average re-start time among 180 machine in a factory after complete shutdown. A random sample of 15 machine was selected and their restart times were recorded. The sample mean and the standard deviation were found to be 3.0 seconds and 0.4 seconds, respectively. 1. Estimate the population mean. (1 mark) 2. Place a bound on the error of estimation (2 Marks) 3. Calculate the 95% confidence interval for the estimated population mean. (2 marks)
Answers
Answer:
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Given:
No of machines = 180
Explanation:
Let
A: Items produced by machine A
B: Items produced by machine B
D: Items detected
We need to find the Probability that the items was produced by machine B, if it is found to be defective
i.e P(B|D)
P(B|D) = P(B) . P(D|B) / [P(B) . P(D|B) + P(A) . P(D|A)]
P(A) = Probability that the items is produced by machine A
= 60% = 60/100 = 0.6
P(B) = Probability that the item is produced by machine B
= 40% = 40/100 = 0.4
P(D|A)= Probability item is defective, if produced by machine A
= 2% = 2/100 = 0.02
P(D|B)= Probability that the items is defective, if produced by machine B
= 1% = 1/100= 0.01
Putting values in formula,
P(B|D)= 0.4× 0.01 / {0.01[ 0.6 × 2 + 0.4]}
= 0.4/(1.2 + 0.4)
= 0.4/1.6
= 4/16
= 1/4
Therefore, required probability is 1/4
Answer = 1/4