 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/14/b/iv/solution

An excess of thirty seconds is

T > 1/2

in minute units. Therefore

P (T > 1/2) = \int_{1/2}^{1} (1 - t) d t = \frac{1}{8} .

This is the shaded triangular area under the probability density function.

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