The height to which a high jumper can clear is normally distributed with mean 1.80 m1.80\text{ m}1.80 m and standard deviation 0.12 m0.12\text{ m}0.12 m.
Using standardisation, show that the probability that this jumper clears less than 1.74 m1.74\text{ m}1.74 m is 0.30850.30850.3085.
This jumper enters a competition. To qualify for the gala, they have up to 3 attempts to clear a height of more than 1.74 m1.74\text{ m}1.74 m. Once they qualify, they do not take any remaining attempts.
Given that they qualified for the gala and that all jumps are independent,
find the probability that this athlete qualified for the gala on their second jump with a height of more than 1.98 m1.98\text{ m}1.98 m.
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.