Study Guide and Intervention (continued) - MathnMind

14-4
Probability Distributions The probabilities associated with every possible value of
the random variable X make up what are called the probability distribution for that
variable. A probability distribution has the following properties.
Properties of a 1. The probability of each value of X is greater than or equal to 0.
Probability Distribution 2. The probabilities for all values of X add up to 1.
The probability distribution for a random variable can be given in a table or in a
probability histogram and used to obtain other information.
Example
NAME ______________________________________________ DATE______________ PERIOD _____
Study Guide and Intervention (continued)
Probability Distributions
The data from the example on page 849 can be used to determine a
probability distribution and to make a probability histogram.
X Number of Siblings P (X )
a. Show that the probability
distribution is valid.
Exercises
0 0.037
1 0.556
2 0.296
3 0.074
4 0.037
For each value of X, the probability
is greater than or equal to 0 and
less than or equal to 1. Also, the
sum of the probabilities is 1.
© Glencoe/McGraw-Hill 850 Glencoe Algebra 1
0.600
0.400
P(X)
0.200
The table at the right shows the probability
distribution for students by school enrollment in the
United States in 1997. Use the table for Exercises 1–3.
1. Show that the probability distribution is valid.
2. If a student is chosen at random, what is the probability
that the student is in elementary or secondary school?
3. Make a probability histogram of the data.
Probability Histogram
0 1 2 3 4
X Number of Siblings
b. What is the probability that a student
chosen at random has fewer than
2 siblings?
Because the events are independent, the
probability of fewer than 2 siblings is the sum of
the probability of 0 siblings and the probability
of 1 sibling, or 0.037 0.556 0.593.
X Type of School P (X )
Elementary 1 0.562
Secondary 2 0.219
Higher Education 3 0.219
Source: The New York Times Almanac
1.0
0.8
P(X) 0.6
0.4
0.2
Probability Histogram
1 2 3
X Type of School