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.
Practise Edexcel A Level Maths Finding the mean and standard deviation with exam-style questions for A Level Maths. 48 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
