An automated sensor records temperature readings from a process that follows a normal distribution. Initially, the process is set with a mean of 55∘C55^{\circ}\text{C}55∘C and a standard deviation of 4.0∘C4.0^{\circ}\text{C}4.0∘C.
Find the probability that a randomly recorded temperature reading is greater than 62∘C62^{\circ}\text{C}62∘C.
The operator changes the mean to μ\muμ but maintains the standard deviation at 4.0∘C4.0^{\circ}\text{C}4.0∘C. The sensor then records 2 independent temperature readings.
The probability that both of these readings are less than 48∘C48^{\circ}\text{C}48∘C is 0.090.090.09.
Find the value of μ\muμ, giving your answer to 1 decimal place.
The calibration is adjusted again so that the mean is 121212 and the standard deviation is 151515.
The sensor then records 4 independent readings from this distribution.
Find the probability that at least one of these readings is negative.
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.