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# S1 - Normal Distribution watch

1. Where did that 0.5 come from? Is it an arbitrary phenomena - will it always be minus 0.5? I can only deduce that it comes from the fact that Z is 1 so 0.5 would eliminate half the probability since the graph doesn't span across the full axis distance.

If anyone could explain/confirm the 0.5 so I can just continue to finish S1 and start with past papers.
2. The probability that P(-2.30<Z<0) is the same as P(0<Z<2.30). To find this you do
P(Z<2.30)- P(Z<0) = 0.9893 - 0.5 = 0.4893.
The probability that P(Z<0) = 0.5 because the area under the whole graph is 1 and it is symmetrical around 0 therefore half of the graph = 1/2= 0.5
3. (Original post by snow leopard)

Where did that 0.5 come from? Is it an arbitrary phenomena - will it always be minus 0.5? I can only deduce that it comes from the fact that Z is 1 so 0.5 would eliminate half the probability since the graph doesn't span across the full axis distance.

If anyone could explain/confirm the 0.5 so I can just continue to finish S1 and start with past papers.
the area under the curve of a normal distribution is = 1
the area of half the space under teh graph will = 0.5

P(-2.3 < Z < 0 )

first he probabilty P(Z<0) is 0.5 because the area under the curve before 0 is 0.5

threfore the probability P(-2.3 < Z) given that Z < 0 will mean you are only looking at half of the graph

so we know that the probabilty of anything less than -2.3 is going to be 0.0107 by looking at your tables for normal distribution

and so anything greater will be 1-0.0107 - 0.9893
but we know that we want probabilty between -2.3 and 0 so anything under -2.3 can be eliminated (0.0107) and anything above 0 can be eliminated (0.5)
so we get 1 - 0.5 - 0.0107
4. Just as I thought, thanks guys ~

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Updated: April 14, 2011
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