A QA engineer is in charge of testing whether or not about 90% of the DVD player
ID: 3307354 • Letter: A
Question
A QA engineer is in charge of testing whether or not about 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, and 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.
What is the probability that the engineer passes a day's production as acceptable if X % of the day's DVD players are faulty ( where X is your age) ? [USE EXCEL, AND SHOW EXCEL STEPS]
X= AGE =53
Explanation / Answer
Ans:
Binomial distribution:
n=12
Let X be the number of DVD players, in a batch of 12 randomly selected DVD players, that fail to meet specications. Then X Bin(12, p) where p is the proportion of DVD players which fail to meet specications in the entire day's production. The engineer passes a day's production as acceptable if X 1.
(a) The probability that the engineer incorrectly passes a day's production as acceptable if p = 0.2
is P(X 1) = =BINOMDIST(1,12,0.2,TRUE)= 0.2749.
(b) The probability that the engineer unnecessarily requires the entire day's production to be tested when p =0.1 is
P(X > 1) = 1 P(X 1) = 1 BINOMDIST(1,12,0.1,TRUE)=1-0.659=0.341