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.
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.