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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.