This document provides examples of calculating deciles from a normal distribution. In example 1, it finds the 4th decile (144.9) for a normal distribution with a mean of 150 and standard deviation of 20. In example 2, it finds the 7th decile (107.8) for a normal distribution with a mean of 100 and standard deviation of 15. It shows the calculations using the normal distribution function and z-values from a standard normal distribution table.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
https://www.slideshare.net/NadeemUddin17
https://nadeemstats.wordpress.com/listofbooks/
DECILES BY USING NORMAL
DISTRIBUTION

3. Example-1
In a normal distribution with µ = 150 and σ = 20 find 𝐷4
Solution:
𝐷4 = 4th deciles, (the points below which 40% area lies and
above which 60% area lies)
Thus P(X ≤ 𝐷4) = 0.40
𝑃
𝑥−𝜇
𝜎
≤
𝐷4−𝜇
𝜎
= 0.40
𝑃 𝑍 ≤
𝐷4−150
20
= 0.40
(from Z- table)
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
- 0.2 0.420
7
0.416
8
0.412
9
0.409
0
0.405
2
0.401
3
0.397
4
0.393
6
0.389
7
0.385
9

4. 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 =
−0.25 − 0.26
2
= −0.255
Hence
𝑃 𝑍 ≤ −0.255 = 0.40
𝐷4−150
20
= −0.255
𝐷4 = 150 + −0.255 20
𝐷4 = 144.9

5. 𝐷7 = 7th deciles, (the points below which 70% area lies and
above which 30% area lies)
Thus P(X ≤ 𝐷7) = 0.70
𝑃
𝑥−𝜇
𝜎
≤
𝐷7−𝜇
𝜎
= 0.70
𝑃 𝑍 ≤
𝐷7−100
15
= 0.70
𝑃 𝑍 ≤ 0.52 = 0.70
(from Z- table)
Example-2
In a normal distribution with µ = 100 and σ = 15 find 𝐷7
Solution:

6. Hence
𝐷7 − 100
15
= 0.52
𝐷7 = 100 + (0.52)(15)
𝐷7 = 107.8