A mechanic has logged the following numbers of hours in maintaining and repairing a certain Detroit Series 6 diesel engine for ten different servicings. \( \begin{array}{llllllll}8.4 & 15.6 & 20.3 & 6.5 & 11.1 & 19.4 & 18.3 & 7.2\end{array} \quad 9.7 \) a. Find the mean for the hours logged. b. Find the median for the hours logged. c. If the mechanic earns \( \$ 17.95 \) per hour, how much does he earn doing the median servicing on this engine? a. The mean for the hours logged is (Type an integer or a decimal.)

Calculate the value by following steps: - step0: Calculate: \(\frac{\left(8.4+15.6+20.3+6.5+11.1+19.4+18.3+7.2+9.7\right)}{10}\) - step1: Remove the parentheses: \(\frac{8.4+15.6+20.3+6.5+11.1+19.4+18.3+7.2+9.7}{10}\) - step2: Add the numbers: \(\frac{116.5}{10}\) - step3: Convert the expressions: \(\frac{\frac{233}{2}}{10}\) - step4: Multiply by the reciprocal: \(\frac{233}{2}\times \frac{1}{10}\) - step5: Multiply the fractions: \(\frac{233}{2\times 10}\) - step6: Multiply: \(\frac{233}{20}\) a. The mean for the hours logged is \( 11.65 \) hours. Now, let's find the median for the hours logged. To find the median, we first need to arrange the hours in ascending order: \( 6.5, 7.2, 8.4, 9.7, 11.1, 15.6, 18.3, 19.4, 20.3 \) Since there are 10 values (an even number), the median will be the average of the 5th and 6th values in this ordered list. Let's calculate the median. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(11.1+15.6\right)}{2}\) - step1: Remove the parentheses: \(\frac{11.1+15.6}{2}\) - step2: Add the numbers: \(\frac{26.7}{2}\) - step3: Convert the expressions: \(\frac{\frac{267}{10}}{2}\) - step4: Multiply by the reciprocal: \(\frac{267}{10}\times \frac{1}{2}\) - step5: Multiply the fractions: \(\frac{267}{10\times 2}\) - step6: Multiply: \(\frac{267}{20}\) b. The median for the hours logged is \( 13.35 \) hours. Now, let's calculate how much the mechanic earns doing the median servicing on this engine. The mechanic earns \( \$ 17.95 \) per hour, so we will multiply the median hours by the hourly rate. Let's calculate the earnings for the median servicing. Calculate the value by following steps: - step0: Calculate: \(13.35\times 17.95\) - step1: Multiply the numbers: \(239.6325\) The mechanic earns approximately \( \$ 239.63 \) for doing the median servicing on this engine. To summarize: - a. The mean for the hours logged is \( 11.65 \) hours. - b. The median for the hours logged is \( 13.35 \) hours. - c. The earnings for the median servicing is approximately \( \$ 239.63 \).