Question

What is the Z score for 95%?

Answer 1

`z=1.65`

Explanation:

Fig-1

Fig-2

Fig-3

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`