Questions: Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to one decimal place as needed.) and months B. We can be 95% confident that the mean length of sentencing for the offense is between and months C. 95% of the sentences for the crime are between and months

Solution Steps

To determine the confidence interval for the mean sentence length, we use the formula:

\[ \bar{x} \pm z \frac{s}{\sqrt{n}} \]

Where:

• \(\bar{x} = 24.5\) (sample mean)
• \(z\) is the z-value corresponding to the desired confidence level (for \(95\%\), \(z \approx 2.0\))
• \(s = 5.2\) (sample standard deviation)
• \(n = 30\) (sample size)

Substituting the values into the formula gives:

\[ 24.5 \pm 2.0 \cdot \frac{5.2}{\sqrt{30}} \]

Calculating the margin of error:

\[ \frac{5.2}{\sqrt{30}} \approx 0.9487 \quad \Rightarrow \quad 2.0 \cdot 0.9487 \approx 1.8974 \]

Thus, the confidence interval is:

\[ 24.5 \pm 1.8974 \]

Calculating the lower and upper bounds:

\[ 24.5 - 1.8974 \approx 22.6026 \quad \text{and} \quad 24.5 + 1.8974 \approx 26.3974 \]

Rounding to one decimal place, we find:

\[ (22.6, 26.4) \]

We can be \(95\%\) confident that the mean length of sentencing for the oilse falls between \(22.6\) and \(26.4\) months.

Final Answer