Question

Trowbridge Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspector for this company believes that a particular process is out of control. Normally, only 71% of all cases are deemed defective due to discolorations.

1. If 8 such cases are sampled, what is the probability that there will be two (2) defective cases if the process is operating correctly

2. What is the probability that there will be more than three (3) defective case?

Answer 1

n = 8, p = 0.71, q = 1 - p = 0.29

The binomial probability formula is P(x) = C(n, x) p^x q^(n - x)

x	P(x) = C(8, x) 0.71^x 0.29^(8 - x)
0	0.0001
1	0.0010
2	0.0084
3	0.0411
4	0.1258
5	0.2464
6	0.3017
7	0.2110
8	0.0646

(a) P(x = 2) = 0.0084

(b) P(x > 3) = P(x = 4) + P(x = 5) + P(x = 6) + P(x = 7) + P(x = 8) = 0.9495

[Please give me a Thumbs Up if you are satisfied with my answer. If you are not, please comment on it, so I can edit the answer. Thanks.]