What is the Z score for 95%?

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Apr 20, 2017

Answer:

#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#

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