1. Think about a density curve that consists of

two straight-line segments. The first goes from

the point (0, 1) to the point (0.7, 1) then the

second goes from the point (0.7, 1) to the point

(1.3, 0).

a. Sketch this density curve:

b. What is the probability that X falls below

0.5?

c. What is the probability that X lies

between 0.7 and 1.3?

d. What is the probability that X lies above

0.2?

e. What is the probability that X is equal to

0.5?

2.Consider a uniform distribution that is defined for 1 X 5 . a. Sketch the distribution. b. What is the probability that X falls below 1.5? c. What is the probability that X lies above 2.5? d. What is the probability that X lies below 1?

4. Prices of condominiums in a certain city are approximately normally distributed with a mean value of about $100,000 and a standard deviation of about $10,000. a. What approximate proportion of the condominiums has a value less than $90,000? b. Give the two values representing the endpoints of the middle 95% of the distribution of condominium prices in this particular city.

5. The heights of American women aged 18 to 24 are approximately normally distributed with mean 65 inches and standard deviation 2.1 inches. Half of all young women are shorter than what height?

6.The length of time needed to complete a certain test is normally distributed with mean 57 minutes and standard deviation 8 minutes. a. What is the relative frequency of people who take between 49 and 65 minutes to complete the test? Sketch the distribution and shade in the area in question. b. Find the interval that contains the middle 95% of completion times for all people taking the test.