Check here for instructional material to complete this problem. Let \( 2.58<\mu<10.2 \) represent an interval on the number line. Complete parts (a) and (b) below. (a) Find the value that is in the middle of the interval. The value is \( \square \). (Type an integer or a decimal. Do not round.)

To find the value in the middle of the interval \( 2.58 < \mu < 10.2 \), you can calculate the midpoint by averaging the two endpoints. The formula for the midpoint is: \[ \text{Midpoint} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2} \] Substituting the values in: \[ \text{Midpoint} = \frac{2.58 + 10.2}{2} = \frac{12.78}{2} = 6.39 \] So, the value in the middle of the interval is \( 6.39 \). --- In statistics, intervals like this are frequently used when determining confidence intervals, where predictions about population parameters (like the mean) are made based on sample data. Understanding how to find midpoints is key to interpreting such data effectively. Common mistakes when calculating midpoints can include misplacing decimal points or forgetting to divide by 2. Always double-check your arithmetic and make sure each step follows logically to avoid errors that could lead to incorrect conclusions in your analysis!