Two swimmers, Alice and Brenda, are training for a 200m freestyle event. Alice’s lap times, in seconds, are normally distributed with mean 42 and variance 4. Brenda’s lap times, in seconds, are normally distributed with mean 43.5 and variance 6. The lap times for Alice and Brenda are independent. Before their heat, they each swim one warm-up lap.
Find the probability that Brenda’s time for the warm-up lap is less than Alice’s.
The final race consists of 50 laps. Assuming that they both start simultaneously and all lap times are independent,
find the probability that Alice beats Brenda in the race by more than 100 seconds.
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.