The weights of a population of adult males are normally distributed with mean μ\muμ kg and standard deviation σ\sigmaσ kg. It is known that 10% of the males weigh more than 95 kg and 2.5% weigh less than 65 kg.
Sketch a diagram to show the distribution of weights represented by this information.
Show that μ=95−1.2816σ\mu = 95 - 1.2816\sigmaμ=95−1.2816σ.
Obtain a second equation involving μ\muμ and σ\sigmaσ, and hence find the value of μ\muμ and the value of σ\sigmaσ to 2 decimal places.
Find the probability that a male chosen at random from the population weighs more than 80 kg.
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.