CAS Exam MAS-II Fall 2019, Question 19
Study guide: Exam MAS-II
You are considering attempting a college entrance exam and would like to understand the percentage of candidates that successfully pass the exam. The alumni have provided you with varying estimates of the percentage of successful candidates. You summarize their responses in the table below:
| Alumni ID | Years since passing the entrance exam | Pass Rate |
|---|---|---|
| 1 | 5 | 70% |
| 2 | 10 | 60% |
| 3 | 20 | 50% |
| 4 | 50 | 40% |
You weight their responses using the reciprocal of the number of years since they passed their entrance exam and this forms your prior distribution of the exam pass rate.
You then poll three graduating seniors from your school and find out that two of those students were successful in passing the exam.
You want to use grid approximation to describe the posterior distribution.
Calculate the posterior probability that the pass rate is 70%.
- A) Less than 50%
- B) Greater than or equal to 50% but less than 55%
- C) Greater than or equal to 55% but less than 60%
- D) Greater than or equal to 60% but less than 65%
- E) Greater than or equal to 65%
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