Standard deviation, Normal Distributions and Taking Random Samples

Click For Summary
SUMMARY

The discussion focuses on calculating the standard score (z-score) for a data value of 9 from a normal distribution with a mean (μ) of 16.8 and a standard deviation (σ) of 2.3. The formula provided for calculating the z-score is z = (x - μ) / σ. By substituting the given values into the formula, users can determine the z-score, which quantifies how many standard deviations the data point is from the mean.

PREREQUISITES
  • Understanding of normal distribution concepts
  • Familiarity with the z-score formula
  • Basic knowledge of mean and standard deviation
  • Ability to perform arithmetic operations
NEXT STEPS
  • Learn how to interpret z-scores in the context of normal distributions
  • Explore the implications of standard deviation in data analysis
  • Study the Central Limit Theorem and its relation to normal distributions
  • Investigate statistical software tools for calculating z-scores, such as R or Python's SciPy library
USEFUL FOR

Students, statisticians, data analysts, and anyone interested in understanding statistical concepts related to normal distributions and z-scores.

DarcyDorian
Messages
1
Reaction score
0
Find the standard score for a the data value 9 from a normal distribution which has a
mean of 16.8 and a standard deviation of 2.3
 
Physics news on Phys.org
Hello and welcome to MHB, DarcyDorian! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Assuming you don't know how to begin, we will need the following formula:

[box=green]
The Normal Distribution​
$z$-score for an $x$-value: $$z=\frac{x-\mu}{\sigma}$$[/box]

Now, we are given $x=9$, $\mu=16.8$ and $\sigma=2.3$, so can you use the above formula to compute $z$ (the standard score)? :)
 

Similar threads

MHB Sampling Distribution of the Sample Means from an Infinite Population
  • · Replies 1 ·
Replies
1
Views
1K
MHB -14.1 ....standard deviation of 15......
  • · Replies 2 ·
Replies
2
Views
1K
MHB What is the probability of exceeding maximum weight with a normal distribution?
  • · Replies 2 ·
Replies
2
Views
2K
MHB This is sampling distribution can you help me with this problem
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What is the significance of standard deviation for arbitrary distributions?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Finance: does the volatility of a stock follow a certain distribution?
  • · Replies 24 ·
Replies
24
Views
4K
High School Is there a relationship between the harmonic mean and the standard deviation?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Statistics Normal Distribution
  • · Replies 2 ·
Replies
2
Views
3K
MHB Statistics-Mean & Standard Deviation of Absences.
  • · Replies 1 ·
Replies
1
Views
2K
MHB Are These Statistics Practice Answers Correct?
  • · Replies 1 ·
Replies
1
Views
2K