In: Statistics and Probability
A cloth manufacturer finds that 8% of their production are defective. What is the probability that a batchof 10 willcontain (a) more than two defectives? (b) Less than seven defectives? (c) Exactly eight defectives.
p = 0.08
n = 10
P(X = x) = 10Cx * 0.08x * (1 - 0.08)10-x
a) P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - (10C0 * 0.080 * 0.9210 + 10C1 * 0.081 * 0.929 + 10C2 * 0.082 * 0.928)
= 1 - 0.9599
= 0.0401
b) P(X < 7) = 1 - (P(X = 8) + P(X = 9) + P(X = 10))
= 1 - (10C8 * 0.088 * 0.922 + 10C9 * 0.089 * 0.921 + 10C10 * 0.0810 * 0.920)
= 1 - 0
= 1
c) P(X = 8) = 10C8 * 0.088 * 0.922 = 0