Math Problem Statement
A set of test scores is skewed to the left, has a mean of 74%, and a standard deviation of 12%. All test scores were between 50 and 100. If Tamia's test score has a Z-score of 1.2, how many standard deviations is Tamia's test score above the mean?
Round your answer to one decimal place.
Solution
The Z-score formula is given by:
where:
- is the Z-score,
- is Tamia's test score,
- is the mean of the test scores,
- is the standard deviation.
In this problem, you are given:
- (Tamia's Z-score),
- (mean),
- (standard deviation).
The Z-score indicates how many standard deviations a data point is above or below the mean. Since Tamia's Z-score is 1.2, her score is 1.2 standard deviations above the mean.
Answer: Tamia's test score is 1.2 standard deviations above the mean.
Would you like further details or have any questions?
Follow-up Questions:
- How do you interpret a negative Z-score?
- What does it mean for a data set to be skewed to the left?
- How would Tamia's Z-score change if her score were lower?
- Can a Z-score be used to compare scores from different tests?
- What does a Z-score of 0 represent in this context?
Tip:
A Z-score of 1.2 indicates that Tamia's score is better than approximately 88% of all test scores, assuming a normal distribution, even though the data is skewed.
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Math Problem Analysis
Mathematical Concepts
Statistics
Z-score
Standard Deviation
Formulas
Z-score formula
Theorems
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Suitable Grade Level
High School
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