Question

Motivation of drug dealers.Consider a study of drug dealers and their motivation for participating in the illegal drug market (Applied Psychology in Criminal Justice, September 2009). The sample consisted of 100 convicted drug dealers who attended a court-mandated counseling program. Each dealer was scored on the Wanting Recognition (WR) Scale, which provides a quantitative measure of a person’s level of need for approval and sensitivity to social situations. (Higher scores indicate a greater need for approval.) The sample of drug dealers had a mean WR score of 39, with a standard deviation of 6. Assume the distribution of WR scores for drug dealers is mound-shaped and symmetric.

a.Give a range of WR scores that will contain about 95% of the scores in the drug dealer sample.

b.What proportion of the drug dealers had WR scores above 51?

c.Give a range of WR sores that contain nearly all the scores in the drug dealer sample.

Short answer

(a) 27 to 51

(b) 2.5%

(c) 21 to 57

Step-by-step solution

Identifying the range where approx. 95% of WR scores will fall

Mean = 39

Standard Deviation = 6

As the data is assumed to be mound-shaped, we will use the Empirical rule.

We know that, 95% measurements fall between 2 standard deviations from mean.

The range will be,

$$\begin{gathered} \overline{x}\pm 2s \\ Upperrange=\overline{x}+2s \\ =39+2\left(6\right) \\ =39+12 \\ =51 \\ Lowerrange=\overline{x}-2s \\ =39-2\left(6\right) \\ =39-12 \\ =27 \end{gathered}$$

Therefore, 95% of the WR scores fall between 27 and 51.

Computing the proportion of scores above 51.

We know that 95% of scores fall between 27 and 51. This only leaves 5% of scores on either sides of the distribution. As the curve is bell shaped and divided by the mean, 2.5% scores will be below 27 and 2.5% scores will be above 51.

Finding the range of scores that contains almost all the scores.

According to the Empirical rule, 99.7% scores should fall between 3 standard deviation and the mean.

$$\begin{gathered} \overline{x}\pm 3s \\ Upperrange=\overline{x}+3s \\ =39+3\left(6\right) \\ =39+18 \\ =57 \\ Lowerrange=\overline{x}-2s \\ =39-3\left(6\right) \\ =39-18 \\ =21 \end{gathered}$$

Therefore, 57-21 is the range where almost all the WR scores will fall.