Answer to Question #110399 in Statistics and Probability for Emmanuel Daniels

Question

The number of typos in a book has a poisson distribution with an average of 5 typos
per 100 pages. What is the probability that you cannot find a typo in 50 pages.

Answer 1

Poisson distribution,

$$P(X=x)=\frac{\lambda^{x} e^{-\lambda}}{x!}$$

$\lambda=5\ typos\ per\ 100 pages\\$

then it converts to 50 pages.

$\lambda=2.5\ typos\ per\ 50 pages$

The probability that you cannot find a typo in 50 pages$(P)=P(X=0)$

$P=\frac{2.5^{0} *e^{-2.5}}{0!}\\ \bold{P=0.0821}$