Module 5: Continuous Random Variables
Section Exercises
Barbara Illowsky & OpenStax et al.
Continuous Probability Functions
1. Which type of distribution does the graph illustrate?
2. Which type of distribution does the graph illustrate?
3. Which type of distribution does the graph illustrate?
4. What does the shaded area represent? P(___< x < ___)
5. What does the shaded area represent? P(___< x < ___)
6. For a continuous probablity distribution, 0 ≤ x ≤ 15. What is P(x > 15)?
7. What is the area under f(x) if the function is a continuous probability density function?
9. A continuous probability function is restricted to the portion between x = 0 and 7. What is P(x = 10)?
10. f(x) for a continuous probability function is 15, and the function is restricted to 0 ≤ x ≤ 5. What is P(x < 0)?
11. f(x), a continuous probability function, is equal to 112, and the function is restricted to 0 ≤ x ≤ 12. What is P (0 < x < 12)?
12. Find the probability that x falls in the shaded area.
13. Find the probability that x falls in the shaded area.
14. Find the probability that x falls in the shaded area.
15. f(x), a continuous probability function, is equal to 13 and the function is restricted to 1 ≤ x ≤ 4. Describe P(x>32).
For each probability and percentile problem, draw the picture.
16. Consider the following experiment. You are one of 100 people enlisted to take part in a study to determine the percent of nurses in America with an R.N. (registered nurse) degree. You ask nurses if they have an R.N. degree. The nurses answer “yes” or “no.” You then calculate the percentage of nurses with an R.N. degree. You give that percentage to your supervisor.
- What part of the experiment will yield discrete data?
- What part of the experiment will yield continuous data?
17. When age is rounded to the nearest year, do the data stay continuous, or do they become discrete? Why?
The Uniform Distribution
Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes.
| 1.5 | 2.4 | 3.6 | 2.6 | 1.6 | 2.4 | 2.0 |
| 3.5 | 2.5 | 1.8 | 2.4 | 2.5 | 3.5 | 4.0 |
| 2.6 | 1.6 | 2.2 | 1.8 | 3.8 | 2.5 | 1.5 |
| 2.8 | 1.8 | 4.5 | 1.9 | 1.9 | 3.1 | 1.6 |
18. The sample mean = 2.50 and the sample standard deviation = 0.8302.
19. The distribution can be written as X ~ U(1.5, 4.5).
20. What type of distribution is this?
21. In this distribution, outcomes are equally likely. What does this mean?
23. What are the constraints for the values of x?
25. What is P(2 < x < 3)?
27. What is P(x = 1.5)?
29. Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet.
30. What is a? What does it represent?
31. What is b? What does it represent?
33. What is the theoretical mean?
35. Draw the graph of the distribution for P(x > 9).
37. Find the 40th percentile.
Use the following information to answer the next eleven exercises. The age o