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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.