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.
228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.