Math Problem Statement
A certain distribution has a mean of 32 and a standard deviation of 4. Find the z-score for a value of 20. Z-Score = [?]
Solution
To find the z-score for a value of 20, use the z-score formula:
where:
- (the value for which we're finding the z-score),
- (the mean of the distribution),
- (the standard deviation).
Substitute the values into the formula:
So, the z-score for a value of 20 is:
Would you like further explanation or have any questions?
Here are some related questions you might find useful:
- How do you interpret a z-score of -3 in terms of standard deviations from the mean?
- What is the probability of finding a value less than 20 in this distribution?
- How would the z-score change if the value were closer to the mean, like 28?
- How does the z-score formula apply to non-normal distributions?
- What does a positive z-score indicate compared to a negative one?
Tip: Remember, a z-score tells you how many standard deviations a value is from the mean, allowing comparisons across different distributions.
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Math Problem Analysis
Mathematical Concepts
Statistics
Normal Distribution
Z-Scores
Formulas
Z-score formula: z = (X - μ) / σ
Theorems
Z-score interpretation in normal distribution
Suitable Grade Level
Grades 9-11
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