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?
We use Poisson's formula:
Pn(k)=λkk!e−λ{P_n}(k) = \frac{{{\lambda ^k}}}{{k!}}{e^{ - \lambda }}Pn(k)=k!λke−λ
λ=np=300⋅0,01=3\lambda = np = 300 \cdot 0,01 = 3λ=np=300⋅0,01=3
Then
P300(5)=355!e−3≈0.1{P_{300}}(5) = \frac{{{3^5}}}{{5!}}{e^{ - 3}} \approx 0.1P300(5)=5!35e−3≈0.1
Answer: 0.1
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