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.
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.