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 1.0, how many standard deviations is Tamia's test score above the mean?

Round your answer to one decimal place.

Your Answer:

Solution

Tamia's Z-score of 1.0 means that her test score is 1 standard deviation above the mean.

Since the problem is asking for how many standard deviations Tamia's test score is above the mean, the answer is simply:

1.0 standard deviation above the mean.

Would you like further details or have any additional questions?

Here are 5 related questions you might consider:

  1. How do you calculate a Z-score in general?
  2. What does it mean for a distribution to be skewed to the left?
  3. If Tamia’s Z-score was -1, how would that affect her position relative to the mean?
  4. What is the relationship between Z-scores and probability?
  5. How do outliers affect the mean and standard deviation?

Tip: A Z-score indicates how many standard deviations a data point is from the mean. Positive Z-scores are above the mean, and negative ones are below the mean.

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Math Problem Analysis

Mathematical Concepts

Statistics
Z-score
Standard Deviation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12