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.
228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.