The random variable M M\,M represents the mass, in grams, of a synthetic gemstone produced in a laboratory. It is known that M M\,M follows a normal distribution with mean 60 and standard deviation 15.
Determine the probability that a randomly selected gemstone has a mass greater than 84 g.
Find the value of k k\,k such that
P(60−k<M<60+k)=0.90 P(60 - k < M < 60 + k) = 0.90 P(60−k<M<60+k)=0.90A single observation mmm, of MMM, is taken. A rectangular label for the gemstone's display case is designed on a coordinate grid with vertices at (0,0)(0, 0)(0,0), (m,0)(m, 0)(m,0), (m,m−20)(m, m - 20)(m,m−20) and (0,m−20)(0, m - 20)(0,m−20), where the units are centimetres.
Find the probability that the area of this label is more than 1500 cm2.
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.