00:01
The first draft of a 200 -page manuscript has 16 typos that are spread randomly across the pages.
00:12
And we are going to assume the number of typos per page follows the poisson distribution.
00:19
So we're going to be determining poisson probabilities and the formula we will use, the probability of x number of typos will be equivalent to lambda to the x power times e to the negative lambda power over x factorial, where lambda represents the average number of typos in the designated number of pages.
00:50
So for the first part of this, we want to determine the probability that there is exactly one typo in the first 20 pages.
01:08
So therefore, if there are 16 typos in 200 pages, then we have to scale that down to determine how many typos, which is our lambda, in the 20 pages.
01:29
So we are scaling down.
01:31
So that means we are dividing by 10.
01:34
So if we divide the 16 by 10, we find out that lambda.
01:40
Is 1 .6.
01:42
So using the formula from up above, we would say 1 .6 to the first power, because this would be our x, and we're multiplying that by e to the negative 1 .6 power, and we are dividing it by 1 .6 power, and we are 288 and your directions were very specific to round to four decimal places...