The discharge duration, D D\,D minutes, of a specialized drone battery is modeled by a normal distribution with a mean of 122.5 minutes and a standard deviation of 3.2 minutes.
Find the probability that a randomly selected battery has a discharge duration exceeding 128 minutes.
Determine the value of d d\,d such that P(122.5<D<d)=0.38P(122.5 < D < d) = 0.38P(122.5<D<d)=0.38.
Two batteries are selected at random from the production line.
Calculate the probability that exactly one of these batteries has a discharge duration between 122.5 minutes and d d\,d 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.