The distance the Zotoc car can travel on 20 litres of fuel is normally distributed with mean 320 km and standard deviation 21.6 km. The distance the Ganmor car can travel on 20 litres of fuel is normally distributed with mean 350 km and standard deviation 7.5 km. Both cars are filled with 20 litres of fuel and are driven towards a place 367 km away.
a) For each car, find the probability that it runs out of fuel before it has travelled 367 km.
b) The probability that a Zotoc car can travel at least $\left( {320 + d} \right){\text{ }}km$ on 20 litres of fuel is 0.409. Find the value of $d$.
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