The duration of a high-precision 3D printing task for a specific mechanical component, SSS, is modelled by a normal distribution with mean 450 seconds and standard deviation 40 seconds.
A technician is scheduled to print a batch of 3 identical components one after another.
Making a reasonable assumption about the printing durations,
find the probability that the total time taken to print the batch of 3 components will exceed 23 minutes.
State the assumption you have made in part (a).
A different 3D printer is used for 'Draft' components. The duration, DDD, for this printer to complete one draft component is modelled by a normal distribution with mean 280 seconds and standard deviation 25 seconds.
The technician must decide whether to start a batch of 3 high-precision components or a batch of 5 draft components.
Using a similar assumption to that made in part (a),
find the probability that the total time taken to print the batch of 3 high-precision components is less than the total time taken to print the batch of 5 draft components.
147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.