1. Assuming that the heights of the Biology students are normally distributed with mean 67 inches and standard deviation of 3.5 inches:

a) What is the probability that a randomly selected student has a height below 64 inches? (2.5 points)

b) What is the probability that a randomly selected student has a height greater than 72 inches? (2.5 points)

c) How many of the students have heights between 62 inches and 75 inches? (2.5 points) d) What is the probability that a randomly selected student has a height exactly 65 inches? (2.5

points)

2. The leopard frog, Rana pipiens, has a sex ratio in most populations of 60 % females and 40 % males.

a) What is the probability that in a random sample of 15 individuals, at most 10 will be female? (2.5 points)

b) What is the probability that in a random sample of 20 individuals, at least 5 are males? (2.5 points)

3. Odonus niger is suggested to come from two lineages which are separated by a large indel in their mtDNA control region. It was found that the 35% of the population of O. niger in Mabini, Batangas belongs to lineage A while the other 65% comes from lineage B. If a sample of 50 O. niger was analyzed for their mtDNA CR, what is the probability that at least 15 individuals will belong to lineage A. (5 points)

4. In an area of heavy infestation, gypsy moths lay egg clusters on trees with a mean number of clusters per tree equal to 4. Calculate the probability that a randomly chosen tree has:

a) no egg clusters (2.5 points) b) at least 3 egg clusters (2.5 points)

5. The average score of students in an exam is 78.53. A sample of 10 students has scores 67, 90, 80,

75, 70, 70, 29, 45, 65, and 70. What is the probability that another 10 students will have a higher score than the first 10 students? Consider up to two decimal places of your t value. (5 points)

6. A reef fish species, the humphead wrasse (Cheilinus undulatus) is seldom encountered in reef surveys (it is only seen in 1 of 100 transects). Supposed that a research team is to conduct a survey and they plan to do 500 transects. What is the probability that they will encounter humphead wrasse: a) in 5 transects? (5 points) b) in at least 20 transects? (5 points)

7. An ornithologist studying turkey vultures, Cathartes aura, measured the lengths of 16 of these

vultures. The following are her data: 70 cm 65 cm 75 cm 60 cm 69 cm 80 cm 84 cm 83 cm 72 cm 88 cm 84 cm 77 cm 76 cm 81 cm 62 cm 75 cm

Calculate the 95 % confidence limits for the mean and provide a brief interpretation (in not more than 1 sentence) (5 points).