Chapter 5: Continuous Random Variables
Chapter 5 Practice
5.1 Practice
Which type of distribution does the graph illustrate?
Solution
Uniform Distribution
Which type of distribution does the graph illustrate?
Which type of distribution does the graph illustrate?
Solution
Normal Distribution
What does the shaded area represent? P(___ < x < ___)
What does the shaded area represent? P(___< x < ___)
Solution
[latex]P(6 \lt x \lt 7)[/latex]
For a continuous probability distribution, [latex]0 \le x \le 15[/latex]. What is [latex]P(x > 15)[/latex]?
What is the area under f(x) if the function is a continuous probability density function?
Solution
one
For a continuous probability distribution, [latex]0 \le x \le 10[/latex]. What is [latex]P(x = 7)[/latex]?
A continuous probability function is restricted to the portion between x = 0 and 7. What is [latex]P(x = 10)[/latex]?
Solution
zero
f(x) for a continuous probability function is [latex]\frac{1}{5}[/latex], and the function is restricted to [latex]0 \le x \le 5[/latex]. What is [latex]P(x \lt 0)[/latex]?
f(x), a continuous probability function, is equal to [latex]\frac{1}{12}[/latex], and the function is restricted to [latex]0 \le x \le 12[/latex]. What is [latex]P (0 \lt x \lt 12)[/latex]?
Solution
one
Find the probability that x falls in the shaded area.
Find the probability that x falls in the shaded area.
Solution
0.625
Find the probability that x falls in the shaded area.
f(x), a continuous probability function, is equal to [latex]\frac{1}{3}[/latex] and the function is restricted to [latex]1\le x \le 4[/latex]. Describe [latex]P (x>\frac{3}{2})[/latex].
Solution
The probability is equal to the area from [latex]x= \frac{3}{2}[/latex] to [latex]x = 4[/latex] above the x-axis and up to [latex]f(x) =\frac{1}{3}[/latex].
5.2 Practice
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 |
The sample mean = 2.50 and the sample standard deviation = 0.8302.
The distribution can be written as [latex]X \sim U(1.5, 4.5)[/latex].
1. What type of distribution is this?
2. In this distribution, outcomes are equally likely. What does this mean?
Solution
It means that the value of x is just as likely to be any number between 1.5 and 4.5.
3. What is the height of f(x) for the continuous probability distribution?
4. What are the constraints for the values of x?
Solution
[latex]1.5 \le x \le 4.5[/latex]
5. Graph [latex]P(2 \lt x \lt 3)[/latex].
6. What is [latex]P(2 \lt x \lt 3)[/latex]?
Solution
0.3333
7. What is [latex]P(x \lt 3.5| x \lt 4)[/latex]?
8. What is [latex]P(x = 1.5)[/latex]?
Solution
zero
9. What is the 90th percentile of square footage for homes?
10. Find the probability that a randomly selected home has more than 3,000 square feet given that