An especially interesting error (with a fair few ramifications) has been discovered in Example 5.6 on pages 122-23. The error was triggered in our calculation of the 99th percentile of the particular Binomial distribution there. Basically we wanted to know the following:
what is the number k for which the probability of tossing at least k heads in 100 tosses is 0.01?Now, because the Binomial is a discrete distribution there is no reason why there should be an integer k for which the probability of tossing at least k heads in 100 tosses is exactly 0.01. In fact it turns out that:
- for k=61 the probability is 0.017
- for k=62 the probability is 0.0105
- for k=63 the probability is 0.006
However, to make the point in the example to work it was important that the probability was LESS than 0.01. So, whereas the example used k=62, what we strictly needed was k=63. This meant all the subsequent calculations were wrong.
There were also some other errors in the example including a couple that had been introduced by the publishers as they were correct in our final manuscript.