Standard Normal Distribution and the z-Score

Health & Medical
Tutor: None Selected Time limit: 1 Day

What is a Z-score and Provide a description of the meaning and use of the z-score.  Give an example that illustrates your answer.  

Sep 3rd, 2015

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Z-Scores is a statistical technique of calculating normal distribution in a set of data.It explains whether a particular score is equal to the mean, below the mean or above the mean of a bunch of scores. They can also tell us how far a particular score is away from the mean. It tries go establish how a score is close to the mean or far away.Given a graph of normal distribution ,we can identify the difference by identifying a Z score by finding the difference between a graph.

for example the point in a disribution curve is 1.6 Then we can find the difference from the centre by subtracting 0.5 if its positive and use the difference to find the z score from the table......,continuing..a minute please please!!

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 3rd, 2015

Thank you so much for assisting me with this question!

Sep 3rd, 2015


It is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions. The standard score does this by converting (in other words, standardizing) scores in a normal distribution to z-scores in what becomes a standard normal distribution. To explain what this means in simple terms, let's use another example ,

given below..... just a minute for a full illustration.

Sep 3rd, 2015


Formula :
X < mean = 0.5-Z
 X > mean = 0.5+Z
 X = mean = 0.5
 Z = (X-m) / σ

where,
 m = Mean.
σ = Standard Deviation.
 X = Normal Random Variable

I think you can now do a math concerning z score,its a comprehensive example showing how z is used in normal distribution.

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Sep 3rd, 2015

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