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 5.98

68. Your stemplot in Exercise 65 suggests that the distribution of lengths of yellow Heliconia flowers is roughly normal. Suppose that the distribution is exactly normal. Use the mean and standard deviation you found in Exercise 67 as the and of the distribution.

  1. What interval of lengths covers the middle 50% of yellow flowers?
  2. What interval of lengths covers the middle 95% of yellow flowers?