3. Fill in the blanks with the appropriate raw scores, z-scores, T-scores, and percentile ranks. Note: the Mean = 50, SD = 5.
Raw z T %ile
35
1.2
35
16
Z = (score-mean)/SD
T = 50 + 10Z
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100 to get percentage.
To fill in the blanks with the appropriate raw scores, z-scores, T-scores, and percentile ranks, we can use the formulas and tables provided.
1. Raw score: The given raw score is 35. This is already provided in the table.
2. Z-score: The z-score represents the number of standard deviations a particular score deviates from the mean. To calculate the z-score, we use the formula:
z = (X - mean) / standard deviation
Given:
X = 35
Mean = 50
Standard Deviation = 5
Substituting the values into the formula:
z = (35 - 50) / 5
z = -15 / 5
z = -3
Therefore, the z-score is -3. This will be filled in the table.
3. T-score: T-scores are a standardized version of the z-scores. To convert the z-score into a T-score, we use the formula:
T = (z * 10) + 50
Given:
z = -3
Substituting the value into the formula:
T = (-3 * 10) + 50
T = -30 + 50
T = 20
Therefore, the T-score is 20. This will be filled in the table.
4. Percentile: The percentile rank represents the percentage of scores that fall below a particular score. To calculate the percentile, we need to consult a z-score table or use software. Since the z-score is given as 1.2, we can use the software to find the corresponding percentile rank.
Using the software, we find that a z-score of 1.2 corresponds to a percentile rank of approximately 88%.
Therefore, the percentile rank is 88. This will be filled in the table.
Now we can fill in the blanks:
Raw Z T %ile
35 -3 20 88