Percentiles by using normal distribution
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This document discusses how to find percentiles using the normal distribution. It provides examples of finding the 45th and 95th percentiles for normal distributions with different mean and standard deviation values. In the first example, the 45th percentile is calculated to be 147.5 for a normal distribution with a mean of 150 and standard deviation of 20. In the second example, the 95th percentile is calculated to be 124.75 for a normal distribution with a mean of 100 and standard deviation of 15. The calculations involve finding the z-score corresponding to the desired percentile and using it to determine the cutoff value.
Percentiles by using normal distribution
- 1. NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS /NadeemUddin17 https://nadeemstats.wordpress.com/listofbooks/ PERCENTILES BY USING NORMAL DISTRIBUTION
- 3. 45 = 45th percentile, (the points below which 45% area lies and above which 55% area lies) Thus P(X 45) = 0.45 モ 45 = 0.45 45150 20 = 0.45 0.125 = 0.45 (from Z- table) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 - 0.1 0.460 2 0.456 2 0.452 2 0.448 3 0.444 3 0.440 4 0.436 4 0.432 5 0.428 6 0.424 7 基ｐ = 0.12 0.13 2 = 0.125 Example-1 In a normal distribution with 袖 = 150 and = 20 find 45 Solution:
- 4. Hence 45150 20 = 0.125 45 = 150 + 0.125 20 45 = 147.5
- 5. Example-2 In a normal distribution with 袖 = 100 and = 15 find 95 Solution: 95 = 95th percentile, (the points below which 95% area lies and above which 5% area lies) Thus P(X 95) = 0.95 モ 95 = 0.95 95100 15 = 0.95 1.65 = 0.95 (from Z- table)
- 6. Hence 95 100 15 = 1.65 95 = 100 + 1.65 15 95 = 124.75