The electrical capacities of standard and long-range battery cells produced for high-performance drones are independently distributed.
The capacity of a standard cell, CsC_sCs, is normally distributed with mean 3200 mAh3200 \text{ mAh}3200 mAh and standard deviation 40 mAh40 \text{ mAh}40 mAh.
The capacity of a long-range cell, ClC_lCl, is normally distributed with mean 6000 mAh6000 \text{ mAh}6000 mAh and standard deviation 90 mAh90 \text{ mAh}90 mAh.
A random variable VVV is defined as the total capacity of three randomly selected standard cells minus the capacity of one randomly selected long-range cell.
V∼N(a,b)V \sim \text{N}(a, b)V∼N(a,b) where aaa and bbb are positive constants.
Determine the value of aaa and the value of bbb.
Calculate the probability that a randomly selected long-range cell has a capacity greater than 1.81.81.8 times the capacity of a single randomly selected standard cell.
A random sample of three standard cells is tested.
Find the probability that the capacity of the first cell in the sample is at least 25 mAh25 \text{ mAh}25 mAh more than the mean capacity of all three cells in the sample.
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.