Hazardous waste: Following is a list of the number of hazardous waste sites in a sample of states of the United States in a recent year. The list has been sorted into numerical order.
\begin{tabular}{llllllllll}
\hline 2 & 5 & 9 & 11 & 12 & 13 & 13 & 13 & 13 & 14 \\
15 & 16 & 19 & 20 & 21 & 25 & 26 & 29 & 30 & 32 \\
32 & 32 & 38 & 40 & 48 & 49 & 52 & 67 & 86 & 116 \\
\hline
\end{tabular}

Source: U.S. Environmental Protection Agency
Send data to Excel
Part 1 of 2
(a) What is the $17^{\text {th }}$ percentile?

The $17^{\text {an }}$ percentile is $\square$.

Part 2 of 2
(b) What is the $62^{\text {nd }}$ percentile?

The $62^{\text {nd }}$ percentile is $\square$.

Step 1 ：Count the number of data points in the list, which is \( N = 30 \)

Step 2 ：Use the formula \( \text{Position} = \frac{P}{100} \times (N + 1) \) to find the position for the 17th percentile, where \( P = 17 \)

Step 3 ：Calculate the position for the 17th percentile, which is \( \text{Position} = \frac{17}{100} \times (30 + 1) = 5.27 \)

Step 4 ：Since the position is not an integer, interpolate between the 5th and 6th data points to find the 17th percentile value

Step 5 ：Calculate the 17th percentile value by taking the average of the 5th and 6th data points, which is \( \frac{11 + 12}{2} = 11.5 \)

Step 6 ：The \( 17^{\text{th}} \) percentile is \( \boxed{11.5} \)

Step 7 ：Use the same formula to calculate the position for the 62nd percentile, where \( P = 62 \)

Step 8 ：Calculate the position for the 62nd percentile, which is \( \text{Position} = \frac{62}{100} \times (30 + 1) = 19.22 \)

Step 9 ：Since the position is not an integer, interpolate between the 19th and 20th data points to find the 62nd percentile value

Step 10 ：Calculate the 62nd percentile value by taking the average of the 19th and 20th data points, which is \( \frac{30 + 32}{2} = 31 \)

Step 11 ：The \( 62^{\text{nd}} \) percentile is \( \boxed{31} \)