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.
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.