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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.