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)00≤x≤6otherwiseShow that k=1324k = \frac{1}{324}k=3241.
Using integration, find
the mean waiting time of a customer,
the probability that a customer will wait for more than 4 minutes.
Three independent customers visit the cafe.
Find the probability that at least 2 of the customers wait for more than 4 minutes.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
