Respuesta :
using the Poisson distribution to determine the probability that a page contains exactly 2 errors is 0.0163
Solution:
Given that, A book contains 400 pages.
There are 80 typing errors randomly distributed throughout the book,
We have to use the Poisson distribution to determine the probability that a page contains exactly 2 errors
The poisson distribution is given as:
[tex]\text { Poisson distribution }=e^{-\lambda} \frac{\lambda^{k}}{k !}[/tex]
[tex]\begin{array}{l}{\text { Where, } \lambda \text { is event rate of distribution for observing k events. }} \\\\ {\text { Here rate of distribution } \lambda=\frac{\text { 80 mistakes }}{400 \text { pages }}=\frac{1}{5}}\end{array}[/tex]
And, k = 2 errors.
Plugging in values in poisson distribution, we get
[tex]\begin{array}{l}{\mathrm{p}(2)=e^{-\frac{1}{5}} \times \frac{\frac{1}{5}^{2}}{2 !}} \\\\ {=2.7^{-\frac{1}{5}} \times \frac{\frac{1}{5^{2}}}{2 \times 1}}\end{array}[/tex]
On solving, we get
= 0.0163
Hence, the probability is 0.0163.
