The deciles of any distribution are the values at the 10th, 20th, ..., 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?

Solution: 

A Normal Distribution is a bell-shaped distribution that represents the probability of the random variable. The total probability under the curve is 1. The standardized random variable in a standard normal distribution is given by:

Z  =  (X - μ) / 𝛔 

The Z value can represent the first and the last deciles of the Standard Normal Distribution. The first decile (10th decile) will be given by the z value:

\(Z_{10th decile}\) = 0.25 (From the Standard  Normal Distribution Table)

The corresponding representation of the 10^th decile is given as:

The last decile (90th decile) will be given by the z value 

\(Z_{90th decile}\)  = 1.64 (From the Standard  Normal Distribution Table)

The corresponding representation of the 90^th decile is given as:

The deciles of any distribution are the values at the 10th, 20th, ..., 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?

Summary:

The first and last deciles of the standard Normal distribution are \(Z_{10th decile}\) = 0.25 and \(Z_{90th decile}\)  = 1.64 respectively.