Chapter 2.2, Problem 65E

To determine

First and last deciles of the standard Normal distribution.

Answer to Problem 65E

First decile:

  $z=-1.28$

Last decile:

  $z=1.28$

Explanation of Solution

Given information:

The deciles of any distribution are the values at the 10^th, 20^th… 90^th percentiles.

Calculations:

First decile:

The first decile possesses the property that 10% of the data values are below it.

Now,

Find the z − score corresponding the probability of 10% (or 0.10) in the normal probability table of the appendix.

Note that

The closest probability would be 0.1003 that lies in the row -1.2 and in the column .08 of the normal probability table.

Then

The corresponding z − score,

  $z=-1.28$

Last decile:

The last decile possesses the property that 90% of the data values are below it.

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

Now,

Find the z − score corresponding the probability of 90% (or 0.90) in the normal probability table of the appendix.

Note that

The closest probability would be 0.8997 that lies in the row 1.2 and in the column .08 of the normal probability table.

Then

The corresponding z − score,

  $z=1.28$