The Probability of Misprints:
Distribution of Misprints in Your Manuscript

by J. M. Haile

The following table gives values from the Poisson distribution for selected values of k, the average number of misprints per page. The entries in the table have been scaled to a manuscript of 100 pages.

To use the table, follow these steps:

  1. From your ms of M total pages, selected 0.1M pages at random. Do not select 0.1M consecutive pages from any part of the ms. But if you like, you may pick an arbitrary integer between 1 and 0.1M; call it A. Then, starting with the Ath page, select every 10th page from the ms.
  2. Read each of your 0.1M pages and count the number of independent misprints; call this number N.
  3. Compute the average: k = N/(0.1M).
  4. Enter the table at your value of k (You may have to round your value to the closest tabulated value.) and read the probabilities P0, P1, P2, and P3.
  5. The probabilities in the table are for a manuscript of 100 pages. To get the values for your ms, multiply each Pn by the factor (M/100).

A sample calculation is given below the table.

Number of pages expected to have n misprints in 100 pages of manuscript
k n = 0 n = 1 n = 2 n = 3
0.02 98.0 2.0 0 0
0.04 96.1 3.8 0.1 0
0.06 94.2 5.7 0.2 0
0.08 92.3 7.4 0.3 0
0.10 90.5 9.0 0.5 0
0.12 88.7 10.6 0.6 0
0.14 86.9 12.2 0.9 0
0.16 85.2 13.6 1.1 0.1
0.18 83.5 15.0 1.4 0.1
0.20 81.9 16.4 1.6 0.1
0.22 80.3 17.7 1.9 0.1
0.24 78.7 18.9 2.3 0.2
0.26 77.1 20.0 2.6 0.2
0.28 75.6 21.2 3.0 0.3
0.30 74.1 22.2 3.3 0.3
0.325 72.3 23.5 3.8 0.4
0.35 70.5 24.7 4.3 0.5
0.375 68.7 25.8 4.8 0.6
0.40 67.0 26.8 5.4 0.7
0.45 63.8 28.7 6.5 1.0
0.50 60.7 30.3 7.6 1.3
Sample Calculation
  1. You have an M = 270-page ms, so you select 0.1(270) = 27 pages at random.
  2. You read those 27 pages and find N = 5 misprints.
  3. So your average is k = 5/27 = 0.185. Round this to 0.18 misprints/page.
  4. From the table at k = 0.18, you read P0 = 83.5, P1 = 15, P2 = 1.4, and P3 = 0.1.
  5. Therefore, your ms is expected to have
83.5(270)/100 = 225 pages with no misprints
15(270)/100 = 41 pages with 1 misprint
1.4(270)/100 = 4 pages with 2 misprints
0.1(270)/100 = 0 pages with 3 or more misprints

One of the more famous applications of the Poisson distribution was published in 1898 by L. von Bortkiewicz, Professor of Economics at the University of Berlin. He found that the Poisson distribution described data documenting the probability that a calvary soldier in the Prussian army would be killed by friendly horse-kick.

Background

Three Little Examples



References

R. W. Hamming, The Art of Probability for Scientists and Engineers, Addison-Wesley, Redwood, CA, 1991.

W. E. Deming, Some Theory of Sampling, Dover, New York, 1966; reprint of 1950 edition published by Wiley.