Answer to Question #169566 in Statistics and Probability for Sakib

Question #169566

A company makes electric motors. The probability an electric motor is malfunctioning is 0.01. What is the probability that a sample of 300 electric motors will contain exactly 5 defective motors?


1
Expert's answer
2021-03-09T02:26:05-0500

We use Poisson's formula:

Pn(k)=λkk!eλ{P_n}(k) = \frac{{{\lambda ^k}}}{{k!}}{e^{ - \lambda }}

λ=np=3000,01=3\lambda = np = 300 \cdot 0,01 = 3

Then

P300(5)=355!e30.1{P_{300}}(5) = \frac{{{3^5}}}{{5!}}{e^{ - 3}} \approx 0.1

Answer: 0.1


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