In the probability distribution to theright, 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

0.263

1

0.581

2

0.125

3

0.026

4

0.004

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

product

sum

mean

of the probabilities is

nothing

.

(Type whole numbers. Use ascendingorder.)

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

Graph the probability distribution. Choose the correct graph below.

A.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

0.5

0.6

NumberofMarriages

Probability

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, 0.58; 5, 0.13.

B.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

0.5

0.6

NumberofMarriages

Probability

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, 0.13; 4, 0.58; 5, 0.26.

C.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

0.5

0.6

NumberofMarriages

Probability

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, 0.58; 2, 0.13; 3, 0.03; 4, 0; 5, 0.

D.

0

1

2

3

4

5

0

0.1

0.2

0.3

0.4

0.5

0.6

NumberofMarriages

Probability

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, 0.58; 1, 0.03; 2, 0; 3, 0.26; 4, 0.13; 5, 0.

Describe the shape of the distribution.

The distribution

is bimodal

has one mode

is multimodal

is uniform

and is

skewed left.

roughly symmetric.

skewed right.

(c) Compute and interpret the mean of the random variable X.

X=

marriages

(Type an integer or a decimal. Do notround.)

Which of the following interpretations of the mean iscorrect?

A.

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

B.

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

C.

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

D.

If many individuals aged 15 year or older weresurveyed, 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.

X=

marriages

(Round to one decimal place asneeded.)

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

(Type an integer or a decimal. Do notround.)

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

(Type an integer or a decimal. Do notround.)

Click to select your answer(s).