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.
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.