IB Maths AI HL AI 4.3 practice question

Question 1

Paper 2Medium5 marks

At a parcel centre, $X$ is the excess handling time, in minutes, for a randomly selected parcel. Figure 1 shows the probability distribution of $X$

(a)

Calculate $\mathrm{E}(X)$ and $\mathrm{Var}(X)$

[3]

(b)

For a parcel with excess handling time $X$ the additional handling charge $Y$ in AUD, is modelled by $Y=3X+2$ Hence determine $\mathrm{E}(Y)$ and $\mathrm{Var}(Y)$

[2]

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