Can Norman beat Lee?

The Herald reports that Russel Norman thinks he can beat Melissa Lee:

The One News Colmar Brunton poll on Sunday gave Labour’s David Shearer a 38-point lead over National’s Melissa Lee.

Dr Norman was six points behind Ms Lee in the poll of 500 residents which had a 4.4 per cent margin of error.

That is not a very helpful statement. The 4.4% margin of error is for a result of 50%. Lee got 15% and Norman got 9%. The margin of error for each (at 95% confidence) is 3.2% and 2.5%.

So what is the probability that Norman actually was ahead of Lee? I have a spreadsheet that calculates these things and it is only 0.21%.

Of course things may change from when the poll was done.