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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 166

The waiting time in minutes, XXX, of a customer at a cafe is modelled by the probability density function

f(x)={kx(36−x2)0≤x≤60otherwise f(x) = \begin{cases} kx(36 - x^2) & 0 \le x \le 6 \\ 0 & \text{otherwise} \end{cases} f(x)={kx(36−x2)0​0≤x≤6otherwise​
a.

Show that k=1324k = \frac{1}{324}k=3241​.

[3]
b.

Using integration, find

the mean waiting time of a customer,

[3]
c.

the probability that a customer will wait for more than 4 minutes.

[2]
d.

Three independent customers visit the cafe.

Find the probability that at least 2 of the customers wait for more than 4 minutes.

[3]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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