Final answer:
Z-scores for the data values 4, 10, and 7 in Mr. Green's normally distributed test with a mean of 6 and standard deviation of 1.5 are -1.33, 2.67, and 0.67, respectively. These scores represent how many standard deviations each value is from the mean.
Step-by-step explanation:
The calculation of z-scores from a normally distributed set of data involves using the mean and standard deviation of the dataset and a specific data value. In Mr. Green's test which was normally distributed with a mean of 6 and a standard deviation of 1.5, we use the formula z = (x - μ) / σ to find the z-scores for the data values 4, 10, and 7.
- For x = 4, the z-score is z = (4 - 6) / 1.5 = -1.33.
- For x = 10, the z-score is z = (10 - 6) / 1.5 = 2.67.
- For x = 7, the z-score is z = (7 - 6) / 1.5 = 0.67.
Z-scores indicate how many standard deviations a value lies from the mean. In this context, a z-score of -1.33 means 4 is 1.33 standard deviations below the mean, a z-score of 2.67 means 10 is 2.67 standard deviations above the mean, and a z-score of 0.67 means 7 is 0.67 standard deviations above the mean.