Statistical analysis of exam passes

Hi, I have some data about some students who have to take a series of 13 exams and are expected to pass a certain number after a set number of 6 month periods. So I have the following table of "expected" passes each 6 month period:

**Exam session** | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

**Number of expected exam passes** | 0 | 1 | 3 | 5 | 7 | 8 | 8 | 9 | 10 | 11 | 12 | 13 | | | | | | |

Then I have the dates of the month that each student passed each exam (which can easily be converted to total number of exams passed at each 6 month period for each student). Eg:

Exam Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |

Passes | | | | 1 | 3 | 5 | 7 | 10 | 10 | 10 | 11 | 11 | 12 | 12 | 13 | 13 | 13 |

(This student clearly not passing fast enough compared to the above table)

What statistical technique would be suitible to analyse whether the above table is reasonable compared to the actual performance of the student, that is, is the expected numbers too harsh, or too lenient given actual students performance?

I am just looking for the name of a relevant technique, wikipedia should suffice for the rest as I am a fairly competent mathematician (just not statistician).

Thanks for any help in advance,

Matt

Re: Statistical analysis of exam passes