The following are the annual salaries of 16 chief executive officers of major companies. (The salaries are written in thousands of dollars. \[ \text { 157, } 700,586,814,134,381,428,181,472,676,75,362,653,542,338,452 \] Send data to calculator Find $25^{\text {th }}$ and $90^{\text {th }}$ percentiles for these salaries. (a) The $25^{\text {th }}$ percentile: $\square$ thousand dollars (b) The $90^{\text {th }}$ percentile: $\square$ thousand dollars

Step 1 ：Given the annual salaries of 16 chief executive officers of major companies in thousands of dollars are: 157, 700, 586, 814, 134, 381, 428, 181, 472, 676, 75, 362, 653, 542, 338, 452.

Step 2 ：First, we need to sort the data in ascending order.

Step 3 ：The sorted salaries are: 75, 134, 157, 181, 338, 362, 381, 428, 452, 472, 542, 586, 653, 676, 700, 814.

Step 4 ：We are asked to find the 25th and 90th percentiles for these salaries.

Step 5 ：The formula for finding the nth percentile is: \(P = \frac{n}{100}*(N + 1)\), where P is the nth percentile, n is the percentile rank we want to find, and N is the total number of data points.

Step 6 ：Substituting n = 25 and N = 16 into the formula, we get \(P_{25} = \frac{25}{100}*(16 + 1) = 4.25\).

Step 7 ：Since 4.25 is not a whole number, we take the floor of 4.25 and use that as the index to find the 25th percentile from the sorted salaries list. The 25th percentile is the 4th value in the sorted list, which is 181 thousand dollars.

Step 8 ：Substituting n = 90 and N = 16 into the formula, we get \(P_{90} = \frac{90}{100}*(16 + 1) = 15.3\).

Step 9 ：Since 15.3 is not a whole number, we take the floor of 15.3 and use that as the index to find the 90th percentile from the sorted salaries list. The 90th percentile is the 15th value in the sorted list, which is 814 thousand dollars.

Step 10 ：Final Answer: (a) The 25th percentile: \(\boxed{181}\) thousand dollars (b) The 90th percentile: \(\boxed{814}\) thousand dollars