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Find Z score of top 5 percentile of a Normal Distribution?

Z Score for the top 5 percentile of a normal distribution is 1.645.

To find the top 5th percentile of a normal distribution, look at the z table. Check the probability closest to 0.05 in the z table. Sometimes the exact values do not exist, in that case, we will consider the best closest value.

In this blog post, we will discuss how to find the top 5 percentile of a standard normal distribution using the z table.

How to Calculate the percentile for z-score?

To find the nth of a normal distribution, follow the below steps:-

Step 1: Go to the Z-table and check the probability closest to the nth (convert it into decimal) in the values inside the table. Sometimes the exact values do not exist, in that case, we will consider the best closest value.

Step 2: Now find the z-score corresponding to the closest value i.e its corresponding row value and its corresponding column value.

Step 3: Combine these numbers as row value + column value.

Conclusion:- The nth percent of the normal distribution will be calculated z-score.

Let’s now find the top 5 percent of a normal distribution using the above steps.

Find the top 5 percentile of a normal distribution

The top 5% of the normal distribution indicates that only 5% of the data lies on the right of the normal standard curve.

So, the minimum percentile required left to the z-score is 95% i.e. (100-5)%

As we know z-table tells us the probability of values less than the given z-score, we will check the 0.95 probability in the Z-table in order to calculate the top 5% of the normal distribution.

To find the z-score for the 95 percentile, we will follow the below steps:

Step 1: Go to the Z-table and check the probability closest to the 0.95 in the values inside the table. Sometimes the exact values do not exist, in that case, we will consider the best closest value.

The closest value to 0.95 in the Z-table is 0.9495 and 0.9505

Step 2: Find the z-score corresponding to this value, its corresponding row value is 1.6 and its corresponding column value is either 0.04 or 0.05

Step 3: Combine these numbers to get the z score value for the 95th percentile as 1.645

Let’s understand how do we calculate the 1.645 value, as we have two corresponding values 1.64 and 1.65 so we sum these numbers and divide by 2 as given below

1.6+0.04 = 1.64 and 1.6 + 0.05 = 1.65

= (1.64 + 1.65)/2

= 1.645

Result: The Z-score for the 95th percentile is 1.645 which means 95 percent of the data values of the normal distribution lies below the 1.645 z-score.

The top 5 percentile of a standard normal distribution is a 1.645 z-score.

Conclusion

I hope the above example to find the top 5 percentile of the normal distribution is helpful to you.

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