# What is the Z score for 95%?

Apr 20, 2017

$z = 1.65$

#### 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 $z = \infty$ [right extreme] and $z = - \infty$[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 $1.6 + 0.05 = 1.65$

$z = 1.65$