Standard +0.3 This is a straightforward application of normal distribution probability calculations requiring standardization to z-scores for two independent cases and comparison. While it involves multiple steps (calculate z-scores for both models, find probabilities, compare), each step uses standard S1 techniques with no conceptual challenges or novel problem-solving required. The 8 marks reflect routine working rather than difficulty.
A company makes two cars, model \(A\) and model \(B\). The distance that model \(A\) travels on 10 litres of petrol is normally distributed with mean 109 km and variance 72.25 km\(^2\). The distance that model \(B\) travels on 10 litres of petrol is normally distributed with mean 108.5 km and variance 169 km\(^2\).
In a trial, one of each model is filled with 10 litres of petrol and sent on a journey of 110 km. Find which model has the greater probability of completing this journey, and state the value of this probability. [8 marks]
A company makes two cars, model $A$ and model $B$. The distance that model $A$ travels on 10 litres of petrol is normally distributed with mean 109 km and variance 72.25 km$^2$. The distance that model $B$ travels on 10 litres of petrol is normally distributed with mean 108.5 km and variance 169 km$^2$.
In a trial, one of each model is filled with 10 litres of petrol and sent on a journey of 110 km. Find which model has the greater probability of completing this journey, and state the value of this probability. [8 marks]
\hfill \mbox{\textit{Edexcel S1 Q2 [8]}}