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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.