Sign In

The normal distribution is a useful statistical tool. One of its practical applications is determining the door height after considering the normal distribution of heights of persons, such that many can pass through it easily without striking their heads. The normal distribution can also determine the probability of a person having a height less than a specific height.

The heights of 15 to 18-year-old males from Chile from 1984 to 1985 followed a normal distribution. The mean height is 172.36 cm, and the standard deviation of 6.34 cm. This information can be used to find the probability of males from Chile having a height of less than 162.85 cm.

Begin by finding the z score for the height of 162.85 cm. After using the formula for the z score, the value is found to be -1.5. From the table for negative z scores, the cumulative area under the curve (from the left of the standard normal distribution) or the probability is found to be 0.0668. Converting this value to a percentage gives 6.68%. It can be concluded that there is a 6.68% probability of males among 15 to 18-year-old males that have a height below 162.85 cm.

Tags

Normal DistributionStatistical ToolApplicationsHeight ProbabilityZ ScoreMean HeightStandard DeviationChilean MalesCumulative AreaProbability Percentage

From Chapter 6:

article

Now Playing

6.12 : Applications of Normal Distribution

Probability Distributions

4.8K Views

article

6.1 : הסתברות בסטטיסטיקה

Probability Distributions

12.0K Views

article

6.2 : משתנים אקראיים

Probability Distributions

11.1K Views

article

6.3 : התפלגות הסתברות

Probability Distributions

6.4K Views

article

6.4 : היסטוגרמות הסתברות

Probability Distributions

10.8K Views

article

6.5 : תוצאות חריגות

Probability Distributions

3.1K Views

article

6.6 : ערך צפוי

Probability Distributions

3.7K Views

article

6.7 : התפלגות הסתברות בינומית

Probability Distributions

10.0K Views

article

6.8 : התפלגות הסתברות פואסון

Probability Distributions

7.7K Views

article

6.9 : התפלגות אחידה

Probability Distributions

4.7K Views

article

6.10 : התפלגות נורמלית

Probability Distributions

10.4K Views

article

6.11 : ציוני z ושטח מתחת לעקומה

Probability Distributions

10.2K Views

article

6.13 : התפלגות הדגימה

Probability Distributions

11.4K Views

article

6.14 : משפט הגבול המרכזי

Probability Distributions

13.5K Views

JoVE Logo

Privacy

Terms of Use

Policies

Research

Education

ABOUT JoVE

Copyright © 2025 MyJoVE Corporation. All rights reserved