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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.