Question

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?

Answer 1

We use Poisson's formula:

${P_n}(k) = \frac{{{\lambda ^k}}}{{k!}}{e^{ - \lambda }}$

$\lambda = np = 300 \cdot 0,01 = 3$

Then

${P_{300}}(5) = \frac{{{3^5}}}{{5!}}{e^{ - 3}} \approx 0.1$

Answer: 0.1