Math Problem Statement
Solution
To convert the given value (48) to a z-score, we can use the z-score formula:
Where:
- (the value we are converting),
- (the mean),
- (the standard deviation).
Now, let's substitute the values into the formula:
Thus, the z-score for 48 is 2.
Would you like further details or have any questions?
Here are 5 related questions:
- What does a z-score of 2 signify in a normal distribution?
- How would you interpret a negative z-score?
- How can z-scores be used to compare data from different distributions?
- What percentage of data falls above a z-score of 2 in a standard normal distribution?
- How would the z-score change if the standard deviation increased to 5?
Tip: Z-scores help determine how far a value is from the mean in terms of standard deviations. A z-score of 2 means the value is 2 standard deviations above the mean.
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Math Problem Analysis
Mathematical Concepts
Statistics
Normal Distribution
Z-score
Formulas
z = (x - μ) / σ
Theorems
Z-Score Theorem
Suitable Grade Level
Grades 10-12
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