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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.