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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.