Finding Areas under the Normal Curve
Finding Areas Under the Normal Curve
1) We can easily find areas like the one below.
[pic]
a) First, find the distance that xi is from the mean and then divide this distance by the size of the standard deviation. The result will be[pic].
[pic]
b) Look up the area in the Z-table.
2) Because the normal cure is symmetric about the mean, repeat step ‘a’ in 1) and look up the absolute value of in the Z-table to find the area.
[pic]
3) In this example you must find two Z values. Find [pic], [pic] and then look up |[pic]| and [pic]in the Z-table to get the areas. Add the two areas together.
[pic]
4) Finding the area in the tail below requires two steps. Remember: we know that the entire area to the right of [pic] is equal to 0.5.
[pic]
a) Find the area under the curve from [pic] to xi in the usual way. We’ll call this area A1.
[pic]
b) Subtract A1 from 0.5. 0.5 – A1 = Area in tail
5) In the example bellow we must find two areas: the area from [pic] to xi (Ai) and the area from [pic] to xj (Aj). Our area of interest will be Aj – Ai.
[pic]
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