Poisson Distribution
Answer 18

No.

Explanation

Jones will lose his job if there is a 1/12 chance or better (p = 0.0833 or higher) that the default rate will reach or exceed 10 in any one month. From the Poisson Table, under the given rate of r = 6 per month, we see that the chance of 10 defaults in one month is 0.0413, or about 1 in 24, a condition that thus will not likely occur, on average, sooner than two years from now. Jones, clever fellow that he is, had in fact consulted that table in making his guarantee.

But wait. He also loses his job if there are more than 10 defaults in any month during the next year, so we must add to this the chances of 11, 12, and more defaults, as long as the table shows a reportable figure. That total (for between 10 and 17 defaults, inclusive) is 0.0838, or approximately 1 in 11.9, just less than 1 in 12. There is thus a slightly better than even chance that Jones will lose his job within the year.

Comment

Mrs Jones should finish work on her teaching certificate. Urgently.

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