The deciles of any distribution are the 10th, 20th,...90th percentiles. The first and last deciles are the 10th and 90th percentiles, respectively.

What are the first and last deciles of the standard
Normal distribution?

HOw would i solve this? thank you sooo much!

To find the first and last deciles of the standard Normal distribution, you can use a table of the standard Normal distribution or a statistical software.

The standard Normal distribution has a mean of 0 and a standard deviation of 1. The first decile represents the value below which 10% of the data falls, and the last decile represents the value below which 90% of the data falls.

Using a standard Normal distribution table or a statistical software, you can find the Z-scores corresponding to the first and last deciles. These Z-scores represent the number of standard deviations from the mean.

For the first decile:
Z = -1.28

For the last decile:
Z = 1.28

To find the actual values corresponding to these Z-scores, you can use the formula:
x = mean + (Z * standard deviation)

For the first decile:
x = 0 + (-1.28 * 1) = -1.28

For the last decile:
x = 0 + (1.28 * 1) = 1.28

So, the first decile is -1.28 and the last decile is 1.28 in the standard Normal distribution.

To find the first and last deciles of the standard Normal distribution, we need to determine the corresponding percentiles.

Step 1: Understand the standard Normal distribution
The standard Normal distribution is a symmetric bell-shaped curve with a mean of 0 and a standard deviation of 1. It is also known as the Z-distribution.

Step 2: Determine the Z-scores
To find the percentiles, we first need to find the Z-scores associated with the desired percentiles. Z-scores represent the number of standard deviations an observation is from the mean.

The first decile corresponds to the 10th percentile, and the last decile corresponds to the 90th percentile.

Using a Z-table or a statistical software, locate the Z-score that corresponds to the 10th and 90th percentile. For the standard Normal distribution, these Z-scores are -1.28 and 1.28, respectively.

Step 3: Convert Z-scores to values
Since the standard Normal distribution has a mean of 0 and a standard deviation of 1, we can convert the Z-scores into values using the formula:

Value = (Z-score * standard deviation) + mean

In this case, the mean is 0, and the standard deviation is 1.

For the first decile:
Value = (-1.28 * 1) + 0 = -1.28

For the last decile:
Value = (1.28 * 1) + 0 = 1.28

Therefore, the first decile of the standard Normal distribution is -1.28, and the last decile is 1.28.

The same as any distribution.