On the first 400 pages of a book, you notice that there are, on average, 10 typos per page. What is the probability that there will be at least 3 typos on page 401? Think about what assumptions you should be making.
I know that the expected value is 10. Do i need to use a normal Approximation or Poisson to try and answer this problem. Any hints would be appreciated. Thanks
Best Answer
I'm assuming you meant "Typos in a book," haha.
You should use the Poisson distribution. The Poisson distribution is appropriate when there are a fixed large number of trials in a given interval (a page, in this case) and each trial has a fixed (usually low) probability. The product of the number of trials and the probability of success (or typo) in each trial is the rate $\lambda$ of the Poisson distribution.
ETA: In the limit, as $\lambda$ increases without bound, the distribution does approach a normal distribution. At $\lambda = 10$, here, the difference is not profound, but it's still more appropriate to use the Poisson distribution.
In actual fact, since the number of characters on a page (i.e., the number of trials on a page) is finite, it might be even more appropriate to use a binomial distribution. However, the difference between the binomial distribution and the Poisson distribution is not significant at this scale, and the Poisson distribution is far easier to compute.