What is the Z score for 95%?

1 Answer
Apr 20, 2017

z=1.65

Explanation:

Fig-1

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Fig-2
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Fig-3

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To obtain the value for a given percentage, you have to refer to the Area Under Normal Distribution Table [Fig-3]

The area under the normal curve represents total probability. It is equal to one or 100%. At the two extremes value of z=oo [right extreme] and z=-oo[left extreme]

Area of one-half of the area is 0.5

Value of z exactly at the middle is 0

We have to find the area for 95% or 0.95

On the one side, we have 0.5 and the remaining 1-0.5=0.45 is on the other side. It may be on either side. If it is on the right-hand side, we will have a positive value of z else negative. Look at the graph.

To find the z value for 0.45, move along the area in the table and locate the nearest value. It is 0.4505 in our table [Fig-3].

First move to the left extreme find the value in the z column. It is 1.6.

Then from the value move vertically up and reach the top most row.
Find the z value. it is 0.05. Add these two values.
It is 1.6+0.05=1.65

z=1.65