Question

I have a scale with a mean of 100 and a SD of 10. Someone gets a raw score of 105 on this scale. Their z score is therefore 0.5

A) True
B) False

Answer 1

The statement is true; the z-score for a raw score of 105 on a scale with a mean of 100 and a standard deviation of 10 is indeed 0.5, indicating the score is 0.5 standard deviations to the right of the mean.

Step-by-step explanation:

The question relates to the calculation of a z-score in statistics. A z-score indicates how many standard deviations a raw score is from the mean of the distribution. Given a mean (μ) of 100 and a standard deviation (σ) of 10 for a normal distribution, the formula to calculate the z-score is z = (X - μ) / σ. For a raw score (X) of 105, the z-score would be z = (105 - 100) / 10 = 0.5. So, the statement that a raw score of 105 corresponds to a z-score of 0.5 is true, meaning that the score of 105 is 0.5 standard deviations to the right of the mean.