Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible…?

...high pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. Compute the following:

a. P(X=5)

b. P(x<=4)

c. The probability that X exceeds its mean value by more than 1 standard deviation.

1 Answer

  • 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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