Wake Technical Community College

### Question Description

I’m working on a Statistics exercise and need support.

A clinical psychologist is administering the Hamilton Rating Scale for Depression (Hamilton, 1967). The scale ranges from 0 to 52. Scoring is based on the 17-item scale and scores of 0–7 are considered as being normal, 8–16 suggest mild depression, 17–23 moderate depression and scores over 24 are indicative of severe depression (Zimmerman, Martinez, Young, Chelminski, & Dalrymple, 2013). We have some evidence about the mean score for the Hamilton Rating Scale for Depression among the population of adolescents: *μ *= 6 with a standard deviation of *σ *=1.5. The clinical psychologist’s patient, a 14-year old girl, scores a 10 on the scale. How would you describe her score relative to the population of adolescents? (Please use your knowledge of z-scores to answer this question.)

Make sure your response is in paragraph form (full sentences, appropriate grammar, punctuation, etc.). Typically 700 words.

References

Hamilton, M. A. X. (1967). Development of a rating scale for primary depressive illness. *British Journal of Social and clinical psychology, 6*(4), 278-296.

Zimmerman, M., Martinez, J. H., Young, D., Chelminski, I., & Dalrymple, K. (2013). Severity classification on the Hamilton depression rating scale. *Journal of Affective Disorders, 150*(2), 384-388.

## Final Answer

please see and give feedback.

The probability density function (PDF) of the normal distribution is:

f ( x) =

−

1

2

2

e

( x− )2

2 2

A normal random variable (X) has following characteristics:

EX = and Var( X ) = 2

( )

A random variable is parameterized by mean ( ) and variance 2 . The mean ( ) is the

center of the distribution and the standard deviation ( ) is the measure of the variation

(

)

around the mean. Thus, a normal random variable is shown as N , 2 . The normal

distribution is a probability function depicting distribution of variable values. It is a

symmetric distribution wherein maximum observations cluster around the mean and the

probabilities for v...