Questions: The following data represent the concentration of dissolved organic carbon ( mg / L ) collected from 20 samples of organic soil. Assume that the population is normally distributed. Complete parts (a) through (c) on the right. 17.50 29.80 27.10 8.81 16.87 20.46 30.91 14.86 5.30 19.80 14.86 8.09 16.51 22.49 14.90 33.67 15.35 9.72 10.30 18.30 (a) Find the sample mean The sample mean is (Round to two decimal places as needed.)

Solution Steps

To find the sample mean \( \mu \) of the given data, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of samples and \( x_i \) represents each individual sample value.

Given the data:

\[ \begin{align_} x_1 & = 17.50 \\ x_2 & = 29.80 \\ x_3 & = 27.10 \\ x_4 & = 8.81 \\ x_5 & = 16.87 \\ x_6 & = 20.46 \\ x_7 & = 30.91 \\ x_8 & = 14.86 \\ x_9 & = 5.30 \\ x_{10} & = 19.80 \\ x_{11} & = 14.86 \\ x_{12} & = 8.09 \\ x_{13} & = 16.51 \\ x_{14} & = 22.49 \\ x_{15} & = 14.90 \\ x_{16} & = 33.67 \\ x_{17} & = 15.35 \\ x_{18} & = 9.72 \\ x_{19} & = 10.30 \\ x_{20} & = 18.30 \\ \end{align_} \]

Calculating the sum of all samples:

\[ \sum_{i=1}^{20} x_i = 355.6 \]

Now, substituting into the formula:

\[ \mu = \frac{355.6}{20} = 17.78 \]

Final Answer