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1 Unit 1: Pure Mathematics A

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Question 102

The duration, T T\,T in hours, of a specific industrial chemical reaction is modeled by the probability density function

f(t)={kt(16−t2)0≤t≤40otherwise f(t) = \begin{cases} kt(16 - t^2) & 0 \le t \le 4 \\ 0 & \text{otherwise} \end{cases} f(t)={kt(16−t2)0​0≤t≤4otherwise​
a.

Show that k=164\displaystyle k = \frac{1}{64}k=641​.

[3]
b.

Using integration, find

the mean duration of the reaction,

[3]
c.

the probability that a reaction lasts for more than 3 hours.

[3]
d.

Three independent reactions are monitored.

Determine the probability that at least 2 of the reactions last for more than 3 hours.

[3]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
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