Answer to Question #209146 in Chemical Engineering for Appu

Question #209146

In a component manufacturing industry, there is a small probability for any 

component to be defective. The components are supplied in packets of . Use 

Poisson approximation to calculate appropriately the number of packets containing 

 (i) at least one defective (ii) at most one defective in a consignment of 100 packets

Expert's answer

The number of defective blades in a packet has binomial distribution 𝐡(𝑛, 𝑝) with

parameters 𝑛 = 100 and 𝑝 = 0.0002

The binomial distribution can be approximated using Poisson with parameter π‘š =

𝑛𝑝 = 0.02

Let 𝑋 equals the number of defective blades in a packet.

Using the formula

we have:

Thus expected frequencies are:

(i) at least one defective 

ii) at most one defective

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