Transcript msv-18 - The Task with Answers

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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, b2).
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!
Now Sam gets
some worrying
news.
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 = 0.2326, so a = 23.3ml.
We now have c = 21.5ml.
With thanks to Pixabay.com
and to Sam Green.
www.making-statistics-vital.co.uk
is written by Jonny Griffiths
[email protected]