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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.