The time taken to wash a car in an automatic bay may be modelled by a normal distribution with mean 300 seconds and standard deviation 25 seconds.
There is a line of 4 cars waiting to be washed.
Making a reasonable assumption about the times taken to wash these cars,
find the probability that the total time taken to wash the 4 cars will be more than 21 minutes.
State the assumption you have made in part (a).
There is also a manual jet-wash station at the facility. The time taken for a customer to use the manual jet-wash may be modelled by a normal distribution with mean 180 seconds and standard deviation 15 seconds.
A customer arrives and must choose between waiting for the 4 cars in the automatic bay or waiting for 6 customers in a queue for the manual jet-wash.
Using a similar assumption to that made in part (a),
find the probability that the total time taken for the 4 cars at the automatic bay will be less than the total time taken for the 6 customers at the manual jet-wash.
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.