Different varieties of the bright tropical flower Heliconia are fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the form of the hummingbirds’ beaks have evolved to match each other. Below are data on the lengths in millimeters of two varieties of these flowers on the island of Dominica. Exercises 65-69 use these data.

238

Heliconia caribaea Red
37.40 38.07 38.87 40.66 41.93
37.78 38.10 39.16 41.47 42.01
37.87 38.20 39.63 41.69 42.18
37.97 38.23 39.78 41.90 43.09
38.01 38.79 40.57
Heliconia caribaea Yellow
34.57 35.45 36.03 36.66 37.02
34.63 35.68 36.11 36.78 37.10
35.17 36.03 36.52 36.82 38.13
Table 5.46: Thanks to Ethan J. Temeles of Amherst College for providing the data. His work is described in Ethan J. Temeles and W. John Kress, Adaptation in a plant-hummingbird association, Science, 300 (2003): 630-633.

Question 5.99

69. Continue to work with the normal distribution of lengths of yellow flowers in Exercise 68. The shortest red flower was 37.4 millimeters long. Using the 68-95-99.7 rule and the location of the quartiles in normal distributions, what can you say about the percentage of yellow flowers that are longer than 37.4 millimeters?

69.

The top 2.5% of the distribution lies above

The top 16% of the distribution lies above

The top 25% of the distribution lies above

The value 37.4 is between 37.155 and 38.13, so between 2.5% and 16% of yellow flowers are longer that 37.4 millimeters.