Question

The assembly line that produces an electronic component of a missile system has historically resulted in a 2% defectiverate. a random sample of 800 components is drawn. what is the probability that the defective rate is greater than 4%? suppose that in the random sample the defective rate is 4%. what does that suggest about the defective rate on the assembly line

Answer 1

Defective rate can be expected to keep an eye on a Poisson distribution. Mean is equal to 800(0.02) = 16, Variance is 16, and so standard deviation is 4.
X = 800(0.04) = 32, Using normal approximation of the Poisson distribution Z1 = (32-16)/4 = 4.
P(greater than 4%) = P(Z>4) = 1 – 0.999968 = 0.000032, which implies that having such a defective rate is extremely unlikely.

If the defective rate in the random sample is 4 percent then it is very likely that the assembly line produces more than 2% defective rate now.