Answer to Question #108378 in Statistics and Probability for Mohammed Moro

Question

The proportion of defective items in a certain manufacturing process is 0.20. If 10 items are selected from the process,find
(a). The expected number of good items.
(b). Probability that none is defective.
(c). Probability that at least 3 are defective.

Answer 1

(a). The expected number of good items.

$P=n\cdot(1-p)=10\cdot0.8=8$

(b). Probability that none is defective.

$P_0=0.8^{10}\approx 0.1074$

(c). Probability that at least 3 are defective.

$P_{>2}=1-P_0-P_1-P_2=1-P_0 - \\C^1_{10}\cdot0.2\cdot0.8^9-C^2_{10}\cdot0.2^2\cdot0.8^8=\\ \approx1-0.1074-0.2684-0.302=0.3222$