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.
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.