Calculate the z-score for each set of data. Determine who did better on her respective test, Tonya or Lisa.
Student English Test Grade z-Score Student Math Test Grade z-Score
John 82 Jim 81
Julie 88 Jordan 85
Samuel 90 Saye 79
Tonya 86 Lisa 82
Mean 86.50 81.75
St. Dev. 3.42 2.50
Given the above information, predict the raw score for a student whose z-score in the Math test is .98.
Didn't I answer this for you previously?
Z = (score-mean)/SD
Compare the Z scores for Tonya and Lisa.
For second question, substitute .98 for the Z score and solve for the raw score. (Are you sure that .98 = Z score and not a proportion of the scores? If so, find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.98) and its corresponding Z score. Again, use the equation above.
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To calculate the Z-score for each set of data, we need to use the formula:
Z = (X - μ) / σ
Where:
- Z is the Z-score
- X is the raw score
- μ is the mean
- σ is the standard deviation
For the English Test:
- Tonya's Z-score = (86 - 86.50) / 3.42 = -0.15
- Lisa's Z-score = (82 - 86.50) / 3.42 = -1.31
For the Math Test:
- Tonya's Z-score = (81 - 81.75) / 2.50 = -0.30
- Lisa's Z-score = (85 - 81.75) / 2.50 = 1.30
Comparing the Z-scores, we can see that Tonya did better than Lisa on both tests. Tonya had a higher Z-score for both the English and Math tests, indicating that her scores were relatively higher compared to the mean and standard deviation of the respective tests.
Now, to predict the raw score for a student whose Z-score in the Math test is 0.98, we can rearrange the Z-score formula:
X = Z * σ + μ
Plugging in the values:
X = 0.98 * 2.50 + 81.75
X ≈ 84.95
Therefore, based on the information provided and using the formula, the predicted raw score for a student with a Z-score of 0.98 in the Math test is approximately 84.95.