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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.