The operational lifespans of deep-sea sensor modules, TTT hours, are normally distributed such that T∼N(μ,402)T \sim \text{N}(\mu, 40^2)T∼N(μ,402).
Given that 15%15\%15% of the modules have a lifespan exceeding 120012001200 hours, calculate the value of μ\muμ correct to the nearest 0.10.10.1 h.
An oceanographer selects 121212 modules at random.
Determine the probability that fewer than 222 of these modules have a lifespan exceeding 120012001200 hours.
A research station deploys 250250250 modules.
By employing a suitable approximation, find the probability that more than 454545 of these modules have a lifespan exceeding 120012001200 hours.
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.