Two editors, Ed and his boss Ada have just finished the proofreading of a new book prior to its publication.
Working independently, Ed detected 25 errors and Ada ended up only with 19.
Provide your estimate (assume what you may) regarding the quantity of errors still remaining after their inspection.
Let's assume that an average editor would find 22 errors (midway between Ed's and Ada's), and that Ed and Ada were one standard deviation from the mean.
Further assume that the high outlier would be two standard deviations above the mean and would consist of finding all the errors, meaning that there are 28 errors.
Now the question becomes, of the three errors not caught by Ed, how many were caught by Ada?
At first blush this might seem to be the expected value of 0, 1, 2 or 3 of the 28 were not in the 19 Ada caught:
Zero caught: (6/28)(5/27)(4/26) = 5/819
1 caught: 3(19/28)(6/27)(5/26) = 95/1092
2 caught: 3(19/28)(18/27)(6/26) = 57/182
3 caught: (19/28)(18/27)(17/26) = 323/1092
The expected number caught would be:
95/1092 + 2*57/182 + 3*323/1092 = 437/273
So the expected value of the number of those 3 missed by Ed to be caught by Ada would be betwee 1 and 2, leaving 2 or 1 undiscovered.
However, it may be that those three errors were particularly hard to spot, which is why Ed missed them. So we might expect more than 1 or 2 to remain undiscovered. Added to the possibility that an outlier might be more than 2 s.d. away from the mean, perhaps we could expect 3 errors to remain undiscovered.

Posted by Charlie
on 20191204 15:30:49 