Question

In: Statistics and Probability

A cloth manufacturer finds that 8% of their production are defective. What is the probability that...

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.

Solutions

Expert Solution

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


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