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 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.