1. The gestation period (length of pregnancy) for the pygmy hippo is normally distributed with a mean of 200 days and a standard deviation of 3.5 day.

(a) What proportion of pygmy hippo pregnancies last more than 203.5 days?

(b) Only about 17% of the pygmy hippo pregnancies last less than _____________ days.

(c) About _______ % of the pygmy hippo pregnancies last more than 200 days.

(d) The middle 68% of pygmy hippo pregnancies last between _________ and ________. (hint... on this one think of the 68-95-99.7 rule).

(e) What proportion of pygmy hippo pregnancies last less than 191 days?

(f) What proportion of pygmy hippo pregnancies last between 194 days and 207 days?

2. The distribution of heights of students in a large class is roughly normal. The average height is 68 inches, and approximately 99.7% of the heights are between 62 and 74 inches.

(a) What is the standard deviation for this distribution? (hint... think of the 68-95-99.7 rule)

(b) What proportion of students in this class would we expect to be taller than 72 inches?

(c) What percentage of students in this class would we expect to be shorter than 70 inches?

(d) What percentage of students in this class would we expect to be between 60 and 65 inches?

(e) How tall would we expect a student to be if that student was as tall or taller than 40% of all the students in this large class?