The time required to manufacture a high-precision gear using a CNC machine is modeled by a normal distribution with a mean of 150 minutes and a standard deviation of 12 minutes.
There are 5 gears currently in the queue to be processed by this machine.
Making a reasonable assumption about the processing times for these gears,
find the probability that the total time taken to process the 5 gears will be more than 13 hours.
State the assumption you have made in part (a).
A semi-automated lathe is also available at the facility. The time required for a gear to be processed on the lathe is modeled by a normal distribution with a mean of 105 minutes and a standard deviation of 10 minutes.
A production manager must decide whether to add a new order to the queue of 5 gears at the CNC machine or to a queue of 7 gears at the semi-automated lathe.
Using a similar assumption to that made in part (a),
find the probability that the total time taken for the 5 gears at the CNC machine will be less than the total time taken for the 7 gears at the semi-automated lathe.
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.