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Deciles The deciles of any distribution are the values at the 10th,20th,,and 90th percentiles. The first and last deciles are the 10th and the 90th percentiles, respectively. What are the first and last deciles of the standard Normal distribution?

Short Answer

Expert verified

First decile:

z=1.28

Last decile:

z=1.28

Step by step solution

01

Given information

The deciles of any distribution are the values at the10th,20th90thpercentiles.

02

Concept

The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.

03

Calculation

First decile:

The first decile has the attribute of having 10%of the data values below it.

Now,

In the normal probability table of the appendix, find the z-score that corresponds to a probability of 10%(or 0.10).

Note that

The probability that comes closest is 0.1003, which is found in row -1.2and column.08of the normal probability table.

Then

The corresponding zscore,

z=1.28

Last decile:

The last decile has the attribute of having 90% of the data values below it.

Similarly, 10%of the data values are above it.

Now,

In the normal probability table of the appendix, find the z-score that corresponds to a probability of 90%(or0.90).

Note that

The probability that comes closest is 0.8997 which is found in row 1.2 and column.08 of the normal probability table.

Then

The corresponding zscore,

z=1.28

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