z-Score Calculator: Standard Normal Distribution
Math Statistics Percentile
z-Score Calculator
Inputs
Left
Right
Left Right Equal Area
Left Right Different Areas
Middle Equal Area
Middle Different Areas
Left z-Score:
Right z-Score
Solution
Left Tail Area:
value
Right Tail Area:
value
Total Area:
value
Percentile/Probability:
value
%
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Description:
This calculator determines the area under the standard normal curve given z-Score values. The area represents probability and percentile values. The calculator allows area look up with out the use of tables or charts. In addition it provide a graph of the curve with shaded and filled area.
What is Z-Score?
The z score is a value calculated using a dataset's standard deviation. Z score measures how many standard deviations a value is above or below the mean. It's used to compare data with other data sets.
It can be calculated using the formula z = (x - m)/s.
The reason that z scores are used because they allow us to compare data. For example, if we have a set of numbers (i.e., test scores), we can use those numbers to see how they relate to each other and compare them.
What is Standard Deviation?
The standard deviation measures how spread out your data points are. It's calculated by finding the square root of the variance, which is just another way to say "average deviation from the mean." So the higher your standard deviation, the more spread out your data points are.
What is the Standard Normal Curve?
The standard normal curve is a bell-shaped curve representing the probability of a normally distributed variable being less than or equal to the given value. The standard normal distribution has a mean of 0 and a standard deviation of 1. It's often called "the bell curve" or the "the unit normal curve."
What is Probability?
Probability is the likelihood of a particular event happening. It's measured as a number between 0 and 1, where 0 represents no chance, and 1 means it's guaranteed to happen. So, for example, if you roll a six-sided die (1/6), there's only one way to get any given number, so its probability is 1/6.
Probability = Number of Ways It Could Happen / Total Number of Possible Outcomes
What is Percentile?
Percentiles are used to rank data. The easiest way to understand this is by thinking about how you would rank students in your class if you gave out report cards. You might give A's only to the top 10% of students, B's only to the next 20%, and so on down until all your students have received a grade.
Percentiles work similarly: they divide scores into 100 groups (or percentiles) so that each group contains exactly 1% of all scores (100/100). This means that if you get a score that places you in the 75th percentile for some test, 75% of other people who took that test had lower scores than yours, and 25% had higher ones.
Fields and Jobs Where Z-Score are Used:
Z score is used in many fields and jobs. For example, it's used by business people, financial analysts, statisticians, and scientists; sports players and coaches; doctors and nurses; engineers and technicians. Z scores are also found in other areas of life, such as education (teacher evaluations), personal finance (credit scores), and consumer behavior research.
Instructions:
- Select area type.
- Adjust z-Score by using the steppers or manually entering the values.
- Note, the solutions will automatically be updated when either of the input date fields are modified or changed.
Area Types:
- Left
- Right
- Left Right Equal Area
- Left Right Different Area
- Middle Equal Area
- Middle Different Area
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