The storage life of a specialized organic catalyst, CCC days, is modeled by a normal distribution with a mean of 45 days and a standard deviation of 8 days.
Calculate the probability that a randomly selected batch of this catalyst lasts longer than 60.0 days.
A 'warning threshold' is set at ddd days, such that the probability of a catalyst failing before this threshold is 0.08. Determine the value of ddd.
A laboratory process requires the catalyst to remain effective for a further 5 days. Given that a specific batch of catalyst has already been stored for 60 days and is still effective, find the probability that it will last until the process is finished.
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.