...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!)(nk)!)
P(X=x) = C(n,x)(p^x)(q^(nx))
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) ≈ 2.738E5 + 4.6E4 + 3.542E3 + 1.653E2 + 5.207E2
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