Question

A researcher is studying a group of American eagles with the following weights: 7.5 lb., 10.2 lb., 9.7 lb., 11.6 lb., 10.0 lb., 9.8 lb., 8.5 lb., 12.1 lb., 9.0 lb., 7.9 lb., 8.8 lb., 11.2 lb. Which weight is at the 90th percentile?

A) 11.6 lb.
B) 12.1 lb.
C) 11.2 lb.
D) 10.2 lb.

Answer 1

To find the 90th percentile weight among the American eagles, the weights are first arranged in ascending order, and then the percentile position is calculated and rounded up to the nearest whole number. The 90th percentile corresponds to the 12th weight in the ordered list, which is 12.1 lb.

Step-by-step explanation:

To determine which weight corresponds to the 90th percentile among the given weights of American eagles, we first arrange the weights in ascending order. Then we calculate the position in the data set that corresponds to the 90th percentile using the formula: P = (N + 1) * (percentile / 100), where P is the position of a given percentile and N is the total number of observations.

The weights in ascending order are: 7.5, 7.9, 8.5, 8.8, 9.0, 9.7, 9.8, 10.0, 10.2, 11.2, 11.6, 12.1 lb.

With 12 observations (N = 12), we calculate the position for the 90th percentile: P = (12 + 1) * (90 / 100) = 13 * 0.9 = 11.7. Since we cannot have a fractional position in a data set, we round up to the nearest whole number, which indicates that we look at the 12th data value for the 90th percentile. Therefore, the 90th percentile corresponds to the 12th weight in the ordered list, which is 12.1 lb.