Math Problem Statement
Find the percentage of all values in a normal distribution for the following z-score.
zless than or equals≤negative 1.94−1.94
Solution
To find the percentage of values in a normal distribution that are less than or equal to , you can follow the same procedure as before.
Result:
Looking up in the Z-table, the cumulative probability corresponding to this z-score is approximately 0.0262.
Interpretation:
This means that approximately 2.62% of the values in a normal distribution are less than or equal to .
Would you like to explore this concept further or have any additional questions?
Here are some related questions you might find helpful:
- How does the area under the curve relate to z-scores?
- What is the z-score for a certain percentile in a normal distribution?
- How can you calculate the probability between two z-scores?
- What is the relationship between z-scores and standard deviations?
- How do you interpret a z-score in terms of standard deviations from the mean?
Tip: Always remember that the Z-table gives you the cumulative probability from the far left up to the specified z-score. For z-scores below zero, this represents the percentage of values that are less than or equal to that z-score in the distribution.
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Math Problem Analysis
Mathematical Concepts
Statistics
Normal Distribution
Formulas
Z-score formula
Cumulative Probability formula
Theorems
Central Limit Theorem
Suitable Grade Level
High School
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