Standard and high-capacity batteries for search drones are independently tested at a facility.
The flight times of standard batteries, SSS, are normally distributed with mean 120 minutes and standard deviation 5 minutes.
The flight times of high-capacity batteries, HHH, are normally distributed with mean 230 minutes and standard deviation 8 minutes.
The random variable W W\,W represents the total flight time provided by 2 randomly selected standard batteries (used sequentially) minus the flight time of 1 randomly selected high-capacity battery.
W∼N(a,b)W \sim \text{N}(a, b)W∼N(a,b) where a a\,a and b b\,b are positive constants.
Find the value of a a\,a and the value of bbb.
Find the probability that a randomly chosen high-capacity battery lasts more than 1.85 times as long as a randomly chosen standard battery.
A random sample of 3 standard batteries is taken.
Find the probability that the flight time of the first standard battery in the sample is at least 3.5 minutes longer than the mean flight time of all 3 standard batteries in the sample.
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.