Final answer:
Using the provided sample mean of 56 and standard deviation of 6 for the 100 convicted drug dealers, the 95% confidence interval for the mean WR score is calculated to be (54.824, 57.176), implying that we are 95% confident the true mean score for all convicted drug dealers would fall within this range.
Step-by-step explanation:
To calculate an interval estimate of the mean WR score for all convicted drug dealers with a 95% confidence level, we can use the formula for the confidence interval for the mean:
CI = \(\bar{x} \pm z\frac{\sigma}{\sqrt{n}}\)
Where \(\bar{x}\) is the sample mean, \(\sigma\) is the standard deviation, \(n\) is the sample size, and \(z\) is the z-score corresponding to the confidence level. Since the sample size (n) is 100, and given \(\bar{x} = 56\) and \(\sigma = 6\), we can find the z-score for a 95% confidence interval from the z-table, which is approximately 1.96. Thus, the confidence interval is calculated as follows:
CI = 56 \pm 1.96 * \(\frac{6}{\sqrt{100}}\)
CI = 56 \pm 1.96 * 0.6
CI = 56 \pm 1.176
Therefore, the confidence interval is (54.824, 57.176).
Interpreting this result, we are 95% confident that the population mean WR score for all convicted drug dealers falls within the interval from 54.824 to 57.176.