(i)[3]
For each car, determine the probability that it uses up all its fuel before covering $367$ km.
(ii)[4]
For a Zotoc car, the probability of travelling at least $(320 + d)$ km on $20$ litres of fuel is $0.409$. Determine the value of $d$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The distance that the Zotoc car can cover on $20$ litres of fuel follows a normal distribution with mean $320$ km and standard deviation $21.6$ km. The distance that the Ganmor car can cover on $20$ litres of fuel follows a normal distribution with mean $350$ km and standard deviation $7.5$ km. Each car is given $20$ litres of fuel and driven towards a destination $367$ km away.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Using standardisation to obtain $z=\frac{367-320}{21.6}$ or $z=\frac{367-350}{7.5}$” …
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