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.
149 exam-style questions on OCR (MEI) A Level Maths 2.4.12 Calculate probabilities from a Normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.