Chapter 6.1, Problem 37E

Giant Tarantulas. 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 a mean of 18.14 mm and a standard deviation of 1.76 mm. Let x denote carapace length for the adult male G. mollicoma.

1. a. Sketch the distribution of the variable x.
2. b. Obtain the standardized version, z, of x.
3. c. Identify and sketch the distribution of z.
4. d. The percentage of adult male G. mollicoma that have carapace length between 16 mm and 17 mm is equal to the area under the standard normal curve between _________ and _________.
5. e. The percentage of adult male G. mollicoma that have carapace length exceeding 19 mm is equal to the area under the standard normal curve that lies to the _________ of _________.