The operational lifespan, in minutes, of high-performance lithium batteries for two different drone models follows normal distributions. Type Alpha batteries have a mean lifespan of 1250 minutes and a standard deviation of 45 minutes. Type Beta batteries have a mean lifespan of 1180 minutes and a standard deviation of 55 minutes.
One battery of each type is selected at random.
Determine the probability that the Type Alpha battery lasts longer than the Type Beta battery.
A fleet of drones is fitted with four Type Alpha and four Type Beta batteries, all operating independently.
Calculate the probability that the total combined lifespan of these eight batteries is greater than 9850 minutes.
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.