the mean is 3.5. dtandard deviation is .5. sally's score is 1.5 on test. how many standard deviations is she from the mean?

billy scores 5. what is his standard score?
what scale of measurement is being used? is it appropriate? why/why not?

To find how many standard deviations Sally's score is from the mean, we can use the formula:

Z = (X - μ) / σ

where:
Z is the number of standard deviations from the mean,
X is the value of the score,
μ is the mean, and
σ is the standard deviation.

Given:
μ (mean) = 3.5
σ (standard deviation) = 0.5
X (Sally's score) = 1.5

Substituting the values into the formula:
Z = (1.5 - 3.5) / 0.5

Calculating:
Z = -2.0 / 0.5

Z = -4.0

Therefore, Sally's score is 4 standard deviations below the mean.

Now, let's move on to Billy's standard score. A standard score, also called a z-score, measures how many standard deviations above or below the mean a particular value is.

To calculate Billy's standard score, we will use the same formula as above:

Z = (X - μ) / σ

Given:
μ (mean) = 3.5
σ (standard deviation) = 0.5
X (Billy's score) = 5

Substituting the values into the formula:
Z = (5 - 3.5) / 0.5

Calculating:
Z = 1.5 / 0.5

Z = 3.0

Therefore, Billy's standard score is 3.0, which means his score is 3 standard deviations above the mean.

Now, let's determine the scale of measurement being used. The information provided does not explicitly state the scale of measurement. However, based on the context of the mean and standard deviation, it is likely that an interval scale is being used. This scale allows for the calculation of means, standard deviations, and z-scores, which are all relevant in this scenario.

As for whether it is appropriate to use this scale, it depends on the context and the characteristics of the data. Generally, an interval scale is appropriate when the intervals between values have consistent meaning and there is no true zero point. For example, in the case of test scores, the intervals between grades (e.g., from 70 to 80) have consistent meaning. However, it is important to note that the appropriateness of a scale depends on the specific analysis or interpretation being made.

The Z score indicates standard deviations from the mean. It is accurate as long as the distribution is normal.

Z = (score - mean)/standard deviation

You can do the calculations.