Question 1202293: a) A company makes tablets of which 85% of tablets would pass a quality control test by an inspector. If an inspector was to pick six tablets at random from a batch and at least four must pass in order for the batch to be approved, what is the probability that the batch passes inspection?
Answer by vashistrs76(1)   (Show Source):
You can put this solution on YOUR website! The probability that the batch passes inspection: 0.9526
Solution:
Number of tablets that pass the inspection, X = 4, 5, 6
n = 6
p = 0.85
q = 1-85 = 0.15
P (x ≥ 4) = P (x =4) + P(x = 5) + P(x = 6)
P (x = r) = (nCr) (p)^r q^(n-r)
P (x = 4) = (6C4) (0.85)^4 (0.15)^(6-4)
P (x = 4) = 0.1762
P (x = 5) = (6C5) (0.85)^5 (0.15)^(6-5)
P (x = 5) = 0.3993
P (x = 6) = (6C6) (0.85)^6 (0.15)^(6-6)
P (x = 6) = 0.3771
P (x ≥ 4) = 0.1762 + 0.3993 + 0.3771
P (x ≥ 4) = 0.9526
Hence, there is a 0.9526 probability that the batch passes inspection.
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