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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.)

Respuesta :

Using the normal distribution, it is found that the girl's score of 10 is higher than 99.62% of the population.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 6, \sigma = 1.5[/tex].

Her z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 6}{1.5}[/tex]

Z = 2.67

Z = 2.67 has a p-value of 0.9962.

Hence her score is higher than 99.62% of the population.

More can be learned about the normal distribution at https://brainly.com/question/25800303

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