The Labor federal government introduced a scheme that put a price on carbon emissions (a "carbon tax") that came into effect on 1 July 2012. This scheme was subsequently dismantled by the Coalition government that won power in September 2013. Prior to the passing of the legislation that put in place the carbon pricing scheme and its dismantling, professional polling organisations such as Newspoll would regularly ask Australian voters whether or not they supported the introduction of a carbon pricing scheme. The results of the poll taken between 12 and 14 July 2013 are available below.

Survey Date	In Favour	Against	Undecided	Sample Size
29 Apr - 1 May 2011	362	651	193	1206
8 Jul - 10 Jul 2011	367	612	245	1224
22 Jul - 24 Jul 2011	450	688	112	1250
21 Oct - 23 Oct 2011	390	720	111	1221
12 Jul - 14 Jul 2013	408	636	156	1200

Suppose that you wanted to construct a 99% confidence interval for the proportion of all voters in favour (TOTAL IN FAVOUR) of a price on carbon, but you were only willing to accept an interval with a total width of 4 percentage points. What is the minimum number of voters that you would need to survey in this case? Show your workings, and explain your answer in words.