A high-precision industrial sensor measures the deviation of a mechanical component's width from a target value. The deviation, DDD microns, follows a normal distribution with a mean of 82 μm82\ \mu\text{m}82 μm and a standard deviation of 6.0 μm6.0\ \mu\text{m}6.0 μm.
Find the probability that a component selected at random has a deviation greater than 95 μm95\ \mu\text{m}95 μm.
The machine is recalibrated so that the mean deviation is μ\muμ but the standard deviation remains at 6.0 μm6.0\ \mu\text{m}6.0 μm. Two independent components are measured by the sensor.
The probability that both components have a deviation of less than 75 μm75\ \mu\text{m}75 μm is 0.160.160.16.
Calculate the value of μ\muμ, giving your answer to 1 decimal place.
A different calibration is tested where the mean deviation is 151515 and the standard deviation is 202020.
The sensor then records 5 independent readings from this distribution.
Determine the probability that the deviation is negative for at least one of these components.
228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.