Please explain how you solved it. It must be done without using software please,
ID: 3295485 • Letter: P
Question
Please explain how you solved it. It must be done without using software please, thank you.
A quality control engineer is in charge of testing whether or not 90% of the DVD players produced by his company conform to specifications. To do this, the engineer randomly selects a batch of 12 DVD players from each day's production. The day's production is acceptable provided no more than 1 DVD player fails to meet specifications. Otherwise, the entire day's production has to be tested. a) What is the probability that the engineer incorrectly passes a day's production as acceptable if only 80% of the day's DVD players actually conform to specification? b) What is the probability that the engineer unnecessarily requires the entire day's production to be tested if in fact 90% of the DVD players conform to specifications?Explanation / Answer
a) P(non defective), p = 0.8
P(defective), q = 1 - p = 0.2
n = 12
P(passing the production as acceptable) = P(no more than 1 fails to meet specification)
= P(11) + P(12)
= 12 x 0.811 x 0.2 + 0.812
= 0.275
b) n = 12
P(non defective), p = 0.9
P(defective), q = 0.1
P(engineer have to test entire days production) = P(more than 1 defctive)
= 1 - P(1 or less defective)
= 1 - P(11 npn defective) - P(12 non defective)
= 1 - 12x0.911x0.1 + 0.912
= 1 - 0.659
= 0.341