Answer :
The 99th percentile of the population is approximately 38.10.
To find the 99th percentile, we first need to arrange the data in ascending order: 18.6, 22.9, 24.3, 26.1, 26.7, 28.3, 31.9, 34.1, 39.3. Next, we calculate the rank of the 99th percentile using the formula:
[tex]\[\text{Rank} = \left(\frac{99}{100}\right) \times (n + 1)\][/tex]
[tex]\[\text{Rank} = \left(\frac{99}{100}\right) \times (9 + 1) = 9.9\][/tex]
Since the rank is not a whole number, we interpolate between the 9th and 10th observations:
[tex]\[\text{99th percentile} = X_{(9)} + (0.9) \times (X_{(10)} - X_{(9)})\][/tex]
[tex]\[\text{99th percentile} = 34.1 + (0.9) \times (39.3 - 34.1) = 38.10\][/tex]
Therefore, the 99th percentile of the population is approximately 38.10. This means that 99% of the data points in the population are less than or equal to 38.10.
Complete Question:
What is the 99th percentile of a population with the given sample data: 26.1, 18.6, 34.1, 28.3, 26.7, 39.3, 31.9, 24.3, 22.9, assuming the population has a bell-shaped distribution?
