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variable x represents the number...

In the following probability distribution, the random variable x represents the number of activities a parent of a Upper KK to 5 th5th-grade student is involved in. Complete parts (a) through (f) below.

x

0

1

2

3

4

P(x)

0.1360.136

0.2470.247

0.2790.279

0.2140.214

0.1240.124

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

This is a discrete probability distribution because the sum of the probabilities is nothing and each probability is (1)

(b) Graph the discrete probability distribution. Choose the correct graph below.

A.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.14; 1, 0.25; 2, 0.28; 3, 0.21; 4, 0.12.

B.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.25; 1, 0.21; 2, 0.14; 3, 0.28; 4, 0.12.

C.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.28; 1, 0.21; 2, 0.12; 3, 0.14; 4, 0.25.

D.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.12; 1, 0.21; 2, 0.28; 3, 0.25; 4, 0.14.

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

The mean is nothing activities.

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

Which of the following interpretations of the mean is correct?

A.

The observed value of an experiment will be equal to the mean of the random variable in most experiments.

B.

As the number of experiments decreases, the mean of the observations will approach the mean of the random variable.

C.

As the number of experiments increases, the mean of the observations will approach the mean of the random variable.

D.

The observed value of an experiment will be less than the mean of the random variable in most experiments.

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

The standard deviation is nothing activities.

(Round to one decimal place as needed.)

(e) What is the probability that a randomly selected student has a parent involved in three activities?

The probability is nothing.

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

(f) What is the probability that a randomly selected student has a parent involved in three or four activities?

The probability is nothing.

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

(1)

between 0 and 1, inclusive.

greater than or equal to 0.

greater than 0 and less than 1.

less than or equal to 1.

x

0

1

2

3

4

P(x)

0.1360.136

0.2470.247

0.2790.279

0.2140.214

0.1240.124

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

This is a discrete probability distribution because the sum of the probabilities is nothing and each probability is (1)

(b) Graph the discrete probability distribution. Choose the correct graph below.

A.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.14; 1, 0.25; 2, 0.28; 3, 0.21; 4, 0.12.

B.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.25; 1, 0.21; 2, 0.14; 3, 0.28; 4, 0.12.

C.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.28; 1, 0.21; 2, 0.12; 3, 0.14; 4, 0.25.

D.

0

1

2

3

4

0

0.1

0.2

0.3

0.4

0.5A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned 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, 0.12; 1, 0.21; 2, 0.28; 3, 0.25; 4, 0.14.

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

The mean is nothing activities.

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

Which of the following interpretations of the mean is correct?

A.

The observed value of an experiment will be equal to the mean of the random variable in most experiments.

B.

As the number of experiments decreases, the mean of the observations will approach the mean of the random variable.

C.

As the number of experiments increases, the mean of the observations will approach the mean of the random variable.

D.

The observed value of an experiment will be less than the mean of the random variable in most experiments.

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

The standard deviation is nothing activities.

(Round to one decimal place as needed.)

(e) What is the probability that a randomly selected student has a parent involved in three activities?

The probability is nothing.

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

(f) What is the probability that a randomly selected student has a parent involved in three or four activities?

The probability is nothing.

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

(1)

between 0 and 1, inclusive.

greater than or equal to 0.

greater than 0 and less than 1.

less than or equal to 1.

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