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.
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.