Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible…?
Each of the 12 refrigerators of a certain type has been returned to a distributor due to an audible high-pitched, oscillating noise when the refrigerator is running. Out of these, 7 refrigerators have a defective compressor, while the other 5 have less serious problems. If the refrigerators are examined in a random order, let X represent the number of defective compressors among the first 6 refrigerators examined.
Compute the following:
a. P(X=5)
b. P(X=6)
1 Answers
n=12, p=7/12, q=5/12
C(n,k) = n!/((k!)(n-k)!)
P(X=x) = C(n,x)(p^x)(q^(n-x))
a. P(X=5) = C(12,5)((7/12)^5)((5/12)^(7)) ≈ 0.1166
b. P(X<=4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
P(X<=4) ≈ 2.738E-5 + 4.6E-4 + 3.542E-3 + 1.653E-2 + 5.207E-2
P(X<=4) ≈ 0.0726
c. The probability that X exceeds its mean value by more than 1 standard deviation.
P(Z<=-1)+P(Z>=1) ≈ 0.317311
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