For quality control purposes, a company that manufactures sim chips for cell/smart phones routinely takes samples from its production process.Since it is important that these chips are nearly fault free, one inspection check involves using microscopic equipment to count the number of imperfections on each chip.Suppose the average number of imperfections per 1000 sim chips is 3.What is the probability that a sample this size (1000 chips) has 2 imperfections?
A)0.4232
B)0.2510
C)0.2240
D)0.5689
E)0.0034

Question

Quizplus · Accepted Answer

The scenario described follows a Poisson distribution, where the average number of imperfections per 1000 sim chips is 3. The probability of observing exactly 2 imperfections in a sample of 1000 chips can be calculated using the Poisson probability formula: P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (3 in this case), k is the number of occurrences (2), and e is the base of the natural logarithm. Plugging in the values gives P(X=2) = (3^2 * e^(-3)) / 2! = 0.2240, which matches choice C.

For Quality Control Purposes, a Company That Manufactures Sim Chips