SOLUTION: A certain electronics company produces a particular type of vacuum tube. It has been observed that, on the average, three tubes of 100 are defective. The company packs the tubes in

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Question 1177793: A certain electronics company produces a particular type of vacuum tube. It has been observed that, on the average, three tubes of 100 are defective. The company packs the tubes in boxes of 400. What is the probability that a certain box of 400 tubes will contain
(a) r defective tubes ?
(b) At least k defective tubes ?
(c) At most one defective tube ?
(d) Interpret your answers to (a), (b), and (c).
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
(a) P%28x+=+r%29=+highlight_green%28400Cr%29%28.03%5Er%29%28.97%29%5E%28400-r%29+
(b) P(x ≥ k) = 1 - P(x ≤ (k-1)) = 1 - highlight_green%28400C%28k-1%29%29%28.03%5E%28k-1%29%29%28.97%29%5E%28n-%28k-1%29%29+
(c) P(x ≤ 1) = binomcdf(400, .03, 1) = .00006
or
P(x=0) + P(x=1)
(c) Expected value .03*400 = 12
in (a) as r approaches 12, P gets larger. In (b) P gets smaller
in (c) the probability is small because x ≤ 1 is so much less that expected value of 12.