Question 4 of 9 , Step 2 of 2 or 10 Correct The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 : Suppose a sample of 405 tenth graders is drawn. Of the students sampled. 337 read above the eighth grade level. Using the data, construct the 905 confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

Step 1 ：The problem is asking for a confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.

Step 2 ：First, we need to find the sample proportion (p̂) of students reading at or below the eighth grade level. This is done by subtracting the number of students reading above the eighth grade level from the total number of students sampled.

Step 3 ：Next, we calculate the standard error of the proportion using the formula \( \sqrt{ \frac{p̂(1 - p̂)}{n} } \), where n is the number of students sampled.

Step 4 ：Finally, we calculate the confidence interval using the formula \( p̂ ± Z \times \text{standard error} \), where Z is the Z-score corresponding to the desired level of confidence (in this case, 90%).

Step 5 ：Given that the total number of students sampled (n) is 405, and the number of students reading above the eighth grade level is 337, we find that the sample proportion (p̂) is approximately 0.168.

Step 6 ：Using this, we calculate the standard error to be approximately 0.019.

Step 7 ：Using a Z-score of 1.645 for a 90% confidence interval, we find that the lower bound of the confidence interval is approximately 0.137 and the upper bound is approximately 0.198.

Step 8 ：Thus, the 90% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is \(\boxed{[0.137, 0.198]}\).