MSV 18: The Coffee Problem

Sam’s cafe is doing well. His coffee machines are dispensing X ml of coffee into a standard cup, where X ~ N(a, b 2 ).

Now Sam gets some worrying news. The owner’s rule is that 98% of standard cups should contain more than c ml of coffee, and Sam’s machines obey this rule, just!

The owner revises their rule so that 99% of standard cups have to contain more than c ml of coffee. Sam does some calculations to find out how he has to adjust his machines.

‘If I increase the mean a by 1%, that will do the trick exactly...’ ‘But looking at it a different way, if I reduce the standard deviation b by 0.1, that will do what’s needed exactly as well!’ Can you find a, b and c? (Give your answers to 3sf.)

Answers

From 1 and 3, 2.054b = 2.326(b - 0.1) so b = 0.855ml. Subtracting 1 from 2, 0.01a = , so a = 23.3ml. We now have c = 21.5ml.

is written by Jonny Griffiths With thanks to Pixabay.com and to Sam Green.