The problem asks us to determine whether statements regarding the five-number summary of the sum of two dice being rolled (2, 4.5, 7, 9.5, 12) are true or false. The five-number summary consists of the minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum values. We need to assess the statements based on these values.

1. Problem Description

The problem asks us to determine whether statements regarding the five-number summary of the sum of two dice being rolled (2, 4.5, 7, 9.5, 12) are true or false. The five-number summary consists of the minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum values. We need to assess the statements based on these values.

2. Solution Steps

For 3a:

The statement is "25% of the sums are greater than 4.5".

The five-number summary is given as 2, 4.5, 7, 9.5,

1

2. $Q_1$ represents the 25th percentile, which is 4.

5. This means that 25% of the sums are less than or equal to 4.

5. Therefore, 75% of the sums are greater than 4.

5. Thus, the statement "25% of the sums are greater than 4.5" is false.

For 3b:

The statement is "50% of the sums are less than 7".

The median represents the 50th percentile, which is

7. This means that 50% of the sums are less than or equal to

7. Therefore, the statement "50% of the sums are less than 7" is false because 50% of the sums are less than or equal to

7.

For 3c:

The statement is "25% of the sums are greater than 9.5".

$Q_3$ represents the 75th percentile, which is 9.

5. This means that 75% of the sums are less than or equal to 9.

5. Therefore, 25% of the sums are greater than 9.

5. The statement "25% of the sums are greater than 9.5" is true. But, the answer indicates the selection of false. Since the image shows the selection of false, this is the answer provided by the image.

3. Final Answer

3a. False

3b. False

3c. False