The mass of the wing case of a mature Emerald Beetle, WWW mg, is modeled by a normal distribution with a mean of 180 mg180\text{ mg}180 mg and a standard deviation of 12 mg12\text{ mg}12 mg.
Determine the probability that the wing case of a randomly captured Emerald Beetle has a mass exceeding 207 mg207\text{ mg}207 mg.
A specimen is classified as 'undersized' if its wing case mass is in the bottom 1.5%1.5\%1.5% of the population. Calculate the maximum mass, www, for a wing case to be classified as undersized.
The mass of the wing case of a Ruby Beetle, MMM mg, is modeled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.
Research indicates that P(M<165)=0.04P(M < 165) = 0.04P(M<165)=0.04 and P(M>210)=0.015P(M > 210) = 0.015P(M>210)=0.015. Find the value of μ\muμ and the value of σ\sigmaσ, giving your answers to two decimal places.
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.