The scores of students in a physics olympiad, SSS, follow a normal distribution. Data shows that 10% of students scored less than 45 marks, and 5% of students scored more than 85 marks.
Calculate the mean score and the standard deviation of the scores.
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.