What is the relationship between Z-scores and probability?

  • Context: MHB 
  • Thread starter Thread starter yourneighbours
  • Start date Start date
  • Tags Tags
    Probability
Click For Summary
SUMMARY

The discussion centers on the relationship between Z-scores and probability within the context of normally distributed data. It establishes that approximately 99% of individuals are located within 2 standard deviations from the mean, which is 30 kilometers with a standard deviation of 8 kilometers. The conversation emphasizes the importance of understanding how to eliminate the extreme lower and upper 0.5% of data to focus on the central tendency. Additionally, it highlights the significance of the empirical rule, which states that 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations from the mean.

PREREQUISITES
  • Understanding of normal distribution and its properties
  • Familiarity with Z-scores and their calculation
  • Knowledge of standard deviation and mean
  • Basic statistics concepts, including the empirical rule
NEXT STEPS
  • Study the calculation and interpretation of Z-scores in statistical analysis
  • Learn about the empirical rule and its applications in real-world scenarios
  • Explore the concept of standard deviation in depth, particularly in relation to data dispersion
  • Investigate the significance of normal distribution in various fields such as psychology and finance
USEFUL FOR

Students, statisticians, data analysts, and anyone interested in understanding the fundamentals of probability and statistics, particularly in relation to normal distribution and Z-scores.

yourneighbours
Messages
1
Reaction score
0
On average, 99% of the people were between ___ and ___kilometers away from their home when they got
into an accident
the mean is 30 with a standard deviation of 8
 
Last edited:
Physics news on Phys.org
Hello and welcome to MHB! :D

Did you mean to use the [SOLVED] prefix for your thread? When you use this, people assume you don't need help.

So, given the symmetry of normally distributed data about the mean, we know we want to eliminate the lower and upper 0.5% of the data.

So, what area do we want associated from the mean to the upper limit?
 
Another way of thinking about what Mark is suggesting is to remember the rule for going 1,2 and 3 standard deviations away from the mean in both directions. 1 SD both ways covers about 68%, 2 covers ______ and 3 covers _______. Have you seen this before?
 

Similar threads

High School Understanding the Interpretation of Z-Scores: Insights and Examples
  • · Replies 11 ·
Replies
11
Views
5K
MHB What percentage of the class scored between a 67% and an 83%
  • · Replies 2 ·
Replies
2
Views
1K
MHB Probability - Amount of money in pocket
  • · Replies 6 ·
Replies
6
Views
2K
MHB How Do You Calculate a Z Score for Toothpaste Effectiveness Testing?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Probability : minutes that customers get served
  • · Replies 5 ·
Replies
5
Views
1K
MHB What is the probability of exceeding maximum weight with a normal distribution?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Calculating Z-Scores for Krabby Patty Sales: Help and Examples
  • · Replies 1 ·
Replies
1
Views
3K
MHB Analyzing Correlation between IQ Scores and GPA in Ninth Graders
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Correct understanding of confidence intervals....
  • · Replies 22 ·
Replies
22
Views
4K
Undergrad Mean time between lottery wins and probability of fraud by organizers
  • · Replies 75 ·
3
Replies
75
Views
8K