A scientific research team uses two types of atmospheric sensors. The operational duration of each sensor is normally distributed. A Type-A sensor has a mean duration of 180 hours and a standard deviation of 8 hours. A Type-B sensor has a mean duration of 42 hours and a standard deviation of 3 hours.
Determine the probability that the duration of a single Type-A sensor exceeds the combined duration of four randomly selected Type-B sensors.
Find the probability that the duration of one Type-A sensor is less than four times the duration of a single, randomly selected Type-B sensor.
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.