In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below. x P(x) 0 0.261 1 0.569 2 0.135 3 0.031 4 0.003 5 0.001 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because all of the probabilities are all of the probabilities are at least one of the probabilities is between nothing and nothing, inclusive, and the mean of the probabilities is nothing. (Type whole numbers. Use ascending order.) (b) Draw a graph of the probability distribution. Describe the shape of the distribution. Graph the probability distribution. Choose the correct graph below. A. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.03; 1, 0; 2, 0; 3, 0.26; 4, 0.57; 5, 0.14. B. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.26; 1, 0.57; 2, 0.14; 3, 0.03; 4, 0; 5, 0. C. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.57; 1, 0.03; 2, 0; 3, 0.26; 4, 0.14; 5, 0. D. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0; 1, 0; 2, 0.03; 3, 0.14; 4, 0.57; 5, 0.26. Describe the shape of the distribution. The distribution ▼ is uniform is multimodal has one mode is bimodal and is ▼ skewed left. skewed right. roughly symmetric. (c) Compute and interpret the mean of the random variable X. μX=nothing marriages (Type an integer or a decimal. Do not round.) Which of the following interpretations of the mean is correct?

In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below. x P(x) 0 0.261 1 0.569 2 0.135 3 0.031 4 0.003 5 0.001 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because all of the probabilities are all of the probabilities are at least one of the probabilities is between nothing and nothing, inclusive, and the mean of the probabilities is nothing. (Type whole numbers. Use ascending order.) (b) Draw a graph of the probability distribution. Describe the shape of the distribution. Graph the probability distribution. Choose the correct graph below. A. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.03; 1, 0; 2, 0; 3, 0.26; 4, 0.57; 5, 0.14. B. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.26; 1, 0.57; 2, 0.14; 3, 0.03; 4, 0; 5, 0. C. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.57; 1, 0.03; 2, 0; 3, 0.26; 4, 0.14; 5, 0. D. 01234500.10.20.30.40.50.6Number of MarriagesProbability A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0; 1, 0; 2, 0.03; 3, 0.14; 4, 0.57; 5, 0.26. Describe the shape of the distribution. The distribution ▼ is uniform is multimodal has one mode is bimodal and is ▼ skewed left. skewed right. roughly symmetric. (c) Compute and interpret the mean of the random variable X. μX=nothing marriages (Type an integer or a decimal. Do not round.) Which of the following interpretations of the mean is correct?

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In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below.		x	P(x)
	0	0.261
	1	0.569
	2	0.135
	3	0.031
	4	0.003
	5	0.001

(a) Verify that this is a discrete probability distribution.

This is a discrete probability distribution because

all of the probabilities are

at least one of the probabilities is

between

nothing

and

nothing,

inclusive, and the

mean

of the probabilities is

nothing.

(Type whole numbers. Use ascending order.)

(b) Draw a graph of the probability distribution. Describe the shape of the distribution.

Graph the probability distribution. Choose the correct graph below.

01234500.10.20.30.40.50.6Number of MarriagesProbability

A histogram has a horizontal x-axis labeled "Number of Marriages" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.6 in intervals of 0.1 has six vertical lines centered on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.03; 1, 0; 2, 0; 3, 0.26; 4, 0.57; 5, 0.14.

01234500.10.20.30.40.50.6Number of MarriagesProbability

Describe the shape of the distribution.

The distribution

▼

is uniform

is multimodal

has one mode

is bimodal

and is

▼

skewed left.

skewed right.

roughly symmetric.

μX=nothing

marriages

(Type an integer or a decimal. Do not round.)

Which of the following interpretations of the mean is correct?

The observed number of marriages will be equal to the mean number of marriages for most individuals.

The observed number of marriages will be less than the mean number of marriages for most individuals.

If any number of individuals aged 15 year or older were surveyed, one would expect the mean number of marriages to be the mean of the random variable.

If many individuals aged 15 year or older were surveyed, one would expect the mean number of marriages to be the mean of the random variable.

(d) Compute the standard deviation of the random variable X.

σX=nothing

marriages

(Round to one decimal place as needed.)

(e) What is the probability that a randomly selected individual 15 years or older was involved in two marriages?

nothing

(Type an integer or a decimal. Do not round.)

(f) What is the probability that a randomly selected individual 15 years or older was involved in at least two marriages?

nothing

(Type an integer or a decimal. Do not round.)

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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