# What is the probability that the professor will not have to create a deferred exam?The final exam in a one-term statistics course is taken in the December exam period.Students who are sick or have...

What is the probability that the professor will not have to create a deferred exam?

The final exam in a one-term statistics course is taken in the December exam period.Students who are sick or have other legitimate reasons for missing the exam are allowed to write a deferred exam scheduled for the first week in January. A statistics professor has observed that only 2% of all students legitimately miss the December final exam. Suppose that the professor has 40 students registered this term.

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### 2 Answers

The final exam in a one-term statistics course is taken in the December exam period. Students who are sick or have other legitimate reasons for missing the exam are allowed to write a deferred exam scheduled for the first week in January. A statistics professor has observed that only 2% of all students legitimately miss the December final exam. Each student has a 2% probability of missing the exam. There are 40 students registered this term for the course. The professor does not have to create a deferred exam if there is no student with a legitimate cause to miss the test.

The probability that a student does not miss a test is 98%. The probability that neither of the 40 students misses the test is 0.98^40 = 0.4457 approximately. This gives the probability that a deferred exam will have to be created as 1 - 0.4457 = 0.5543

**There is a 55.43% probability that a deferred exam need not be created.**

The question is what is the probability that the professor will not have to create a deferred exam?