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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