MSV 18: The Coffee Problem
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MSV 18: The Coffee Problem www.making-statistics- vital.co.uk
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www.making-statistics-vital.co.uk. 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 ). The owner’s rule is that 98% of standard cups should contain more than c ml of coffee, - PowerPoint PPT Presentation
Transcript of MSV 18: The Coffee Problem
MSV 18: The Coffee Problem
www.making-statistics-vital.co.uk
Sam’s cafe is doing well.
His coffee machines are dispensing X ml of coffee
into a standard cup, where X ~ N(a, b2).
Now Sam gets some worrying
news.
The owner’s rule is that 98% of standard cupsshould 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 calculationsto 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 deviationb 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 = 0.2326, so a = 23.3ml.
We now have c = 21.5ml.
www.making-statistics-vital.co.uk
is written by Jonny Griffiths
With thanks to Pixabay.comand to Sam Green.
