Carpenter Ants II

Suppose that the distribution of number of Carpenter Ants (Camponotus spp.) in a nest is known to be N(1400,300). In the previous assignment you identified the type of question (e.g., “forward-left”, “reverse-between”) for each question below. In this assignment you should answer each the question (provide a numeric answer and include a quick drawing and the R code that you used).

  1. What percentage of nests have more than 1900 ants?
  2. What is the number of ants such that 15% of nests have more ants?
  3. What is the number of ants such that 33% of nests have fewer ants?
  4. What percentage of nests have between 700 and 1900 ants?
  5. What percentage of nests have fewer than 300 ants?
  6. What is the number of ants such that 5% of nests have more ants?
  7. The most common 80% of nests have between what two numbers of ants?


SAT Scores

SAT scores are approximately normal with a mean of 550 and standard deviation of 65. School A accepts students with a score of 500 or better. School B accepts students with a score of 650 or better. Use this information to answer the questions below (include a quick drawing and the R code that you used).

  1. What type of variable is SAT score?
  2. What proportion of students cannot get accepted by School A?
  3. What percentage of students can get accepted by School B?
  4. What percentage of students can get accepted by School A BUT NOT by School B?
  5. What score should School C use so that only 25% of students can get accepted?


Urban Deer Relocations

Relocation methods for controlling the overpopulation of Whitetail Deer (Odocoileus virginianus) in urban areas is controversial. Animal rights organizations like the idea because they believe deer are unharmed in this manner, but scientists suspect that translocation can have a higher mortality rate than hunting or culling. On this note, researchers in Wanakena, New York wanted to examine the home-range sizes of resident and translocated female deer (Jones et al. 1997). The average home range size was 0.30 km2, with a standard deviation of 0.095 km2, for 39 translocated does in the Dubuar Forest between 1994 and 1995. Assume that the distribution of home range sizes is normal. Use this information to answer the questions below (include a quick drawing and the R code that you used).

  1. What proportion of deer have home range sizes between 0.2 and 0.4 km2?
  2. What proportion of deer have a home range size greater than 0.32 km2?
  3. How big is the home range such that 17% of deer have a larger home range?
  4. How big is the home range such that 32% of deer have a smaller home range?
  5. What proportion of deer have a home range size less than 0.4 km2?
  6. Between what two sizes of home ranges do the most common 48% of deer inhabit?