Figure 511 the cumulative distribution function cdf

Figure 5.11
The cumulative distribution function (cdf) of X is defined by P ( X ≤ x ). It is a function of x that gives the probability that
the random variable is less than or equal to x .
FORMULA REVIEW
5.1 Continuous Probability Functions
Probability density function (pdf) f ( x ):
• f ( x ) ≥ 0
• The total area under the curve f ( x ) is one.
Cumulative distribution function (cdf): P ( X ≤ x )
PRACTICE
Chapter 5 | Continuous Random Variables 201

5.1 Continuous Probability Functions
1. Which type of distribution does the graph illustrate?
Figure 5.12
2. Which type of distribution does the graph illustrate?
Figure 5.13
3. Which type of distribution does the graph illustrate?
Figure 5.14
202 Chapter 5 | Continuous Random Variables
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4. What does the shaded area represent? P (___< x < ___)
Figure 5.15
5. What does the shaded area represent? P (___< x < ___)
Figure 5.16
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?
8. For a continuous probability distribution, 0 ≤ x ≤ 10. What is P ( x = 7)?
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
1
5
, and the function is restricted to 0 ≤ x ≤ 5. What is P ( x < 0)?
11. f ( x ), a continuous probability function, is equal to
1
12
, and the function is restricted to 0 ≤ x ≤ 12. What is P (0 < x <
12)?
Chapter 5 | Continuous Random Variables 203

12. Find the probability that x falls in the shaded area.
Figure 5.17
13. Find the probability that x falls in the shaded area.
Figure 5.18
14. Find the probability that x falls in the shaded area.
Figure 5.19
15. f ( x ), a continuous probability function, is equal to
1
3
and the function is restricted to 1 ≤ x ≤ 4. Describe P
⎛
⎝
x >
3
2
⎞
⎠
.
HOMEWORK
204 Chapter 5 | Continuous Random Variables
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5.1 Continuous Probability Functions
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.
a. What part of the experiment will yield discrete data?
b. 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?
SOLUTIONS
1 Uniform Distribution
3 Normal Distribution
5 P (6 < x < 7)
7 one
9 zero
11 one
13 0.625
15 The probability is equal to the area from x =
3
2
to x = 4 above the x-axis and up to f ( x ) =
1
3
.
17 Age is a measurement, regardless of the accuracy used.
Chapter 5 | Continuous Random Variables 205