One of the larger species of tarantulas is the Grammostola mollicoma, whose common name is the Brazilian giant tawny red. A tarantula has two body parts. The anterior part of the body is covered above by a shell, or carapace. From a recent article by F. Costa and F. Perez–Miles titled “Reproductive Biology of Uruguayan Theraphosids” (The Journal of Arachnology, Vol. 30, No. 3, pp. 571–587), we find that the carapace length of the adult male G. mollicoma is normally distributed with mean 18.14 mm and standard deviation 1.76 mm.
a. Find the percentage of adult male G. mollicoma that have carapace length between 16 mm and 17 mm.
b. Find the percentage of adult male G. mollicoma that have carapace length exceeding 19 mm.
c. Determine and interpret the quartiles for carapace length of the adult male G. mollicoma.
d. Obtain and interpret the 95th percentile for carapace length of the adult male G. mollicoma.