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Mr. green’s test was normally distributed with a mean of 6 and a standard deviation of 1.5. Find each z-scores for each of the following data values.

(a) 4
(b) 10
(c) 7

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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.

User Jithu Reddy
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