A study of the Consideration of Future Consequences(CFC) scale found a mean score of 3.51, with a standard deviation of 0.61, for the 664 students in the sample(Petrocelli, 2003). For the sake of this exercise, let’s assume
that this particular sample comprises the entire population of interest.
a. If your CFC score is 4.2, what is your z score? Use symbolic notation and the formula. Explain why this answer makes sense.
b. If your CFC score is 3.0, what is your z score? Use symbolic notation and the formula. Explain why this answer makes sense.
c. If your z score is 0, what is your CFC score? Explain
Use same process as indicated in previous post.
a. To find the z-score for a given CFC score of 4.2, we can use the formula:
z = (X - μ) / σ
Where:
X = CFC score (4.2 in this case)
μ = population mean (3.51)
σ = population standard deviation (0.61)
Substituting the values into the formula, we get:
z = (4.2 - 3.51) / 0.61
z ≈ 1.13
Therefore, the z-score for a CFC score of 4.2 is approximately 1.13.
This answer makes sense because the z-score measures the number of standard deviations a particular data point is away from the mean. In this case, a CFC score of 4.2 is higher than the mean (3.51), indicating that it is above average. The positive z-score (greater than 0) suggests that the score is above the mean as well.
b. Using the same formula, we can calculate the z-score for a CFC score of 3.0:
z = (X - μ) / σ
Substituting the values:
z = (3.0 - 3.51) / 0.61
z ≈ -0.84
The z-score for a CFC score of 3.0 is approximately -0.84.
This answer also makes sense because a CFC score of 3.0 is below the mean (3.51), resulting in a negative z-score. A negative z-score indicates that the data point is below average or below the mean.
c. When the z-score is 0, it means that the data point is exactly at the mean. So, if your z-score is 0, your CFC score would be equal to the mean CFC score (μ).
In this case, if the z-score is 0, your CFC score would be equal to 3.51, which is the mean CFC score of the population.
This makes sense because a z-score of 0 indicates that your score is exactly average or at the mean of the population distribution.