 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2021-resit/7/b/iii/solution

Subtract the two values of the survival function, or integrate the probability density function directly:

P (14 < T < 30) = \int_{14}^{30} \frac{1}{25} e^{- t /25} d t = e^{- 14/25} - e^{- 30/25} = 0.270 (three significant figures) .

The final zero records the requested third significant figure.

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