The charging time, CCC minutes, of a high-performance industrial drone battery is modelled by a normal distribution such that C∼N(150,σ2)C \sim \text{N}(150, \sigma^2)C∼N(150,σ2). Quality control tests indicate that 6.68% of these batteries take longer than 180 minutes to reach full capacity.
Determine the value of the standard deviation, σ\sigmaσ.
A logistics facility purchases a batch of 30 such batteries.
Calculate the probability that more than 4 of these batteries take longer than 180 minutes to charge.
An international shipping company operates 120 such facilities, each equipped with a batch of 30 batteries.
Using a suitable Poisson approximation, estimate the probability that at least 3 of these facilities have more than 4 batteries that take longer than 180 minutes to charge.
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.