Question

a researcher tracks data about the outgoing mail in a large office. you want to complete the two-way frequency table to show the researcher’s results. complete parts a and b.

type of delivery
type | regular | overnight | total
letter | | 5 | 35
package | 25 | | 55
total | | | 55

a. complete the two-way frequency table to show the researcher’s results.

type of delivery
type | regular | overnight | total
letter | 15 | 5 | 20
package | 25 | 10 | 35
total | 40 | 15 | 55

b. which type of outgoing mail is delivered from the office less frequently? explain. select the correct choice and fill in the answer boxes to complete the choice

○ a. letters are delivered less frequently than packages based on the office’s outgoing mail. there are a total of □ packages and □ letters in the outgoing mail.

○ b. packages are delivered less frequently than letters based on the office’s outgoing mail. there are a total of □ packages and □ letters in the outgoing mail.

Explanation:

Part a: Completing the Two - Way Frequency Table

Step 1: Find the number of regular letters

We know that for letters, the total number of letters is the sum of regular and overnight letters. Let the number of regular letters be \(x\). We have the equation \(x + 5=20\) (from the total for letters in the completed table). Solving for \(x\), we subtract 5 from both sides: \(x=20 - 5=15\).

Step 2: Find the number of overnight packages

For packages, the total number of packages is the sum of regular and overnight packages. Let the number of overnight packages be \(y\). We know that the total number of packages is 35 and the number of regular packages is 25. So, \(25 + y=35\). Subtracting 25 from both sides, we get \(y = 35-25 = 10\).

Step 3: Find the total number of regular deliveries

The total number of regular deliveries is the sum of regular letters and regular packages. So, \(15+25 = 40\).

Step 4: Find the total number of overnight deliveries

The total number of overnight deliveries is the sum of overnight letters and overnight packages. So, \(5 + 10=15\).
The completed table is:

Type	Regular	Overnight	Total
Package	25	10	35
Total	40	15	55

Part b: Determining the Less Frequent Mail Type

Step 1: Compare the total number of letters and packages

From the table, the total number of letters is 20 and the total number of packages is 35. Since \(20<35\), letters are delivered less frequently than packages.

Step 2: Fill in the blanks

There are a total of 35 packages and 20 letters in the outgoing mail. So the correct option is A. Letters are delivered less frequently than packages based on the office’s outgoing mail. There are a total of \(\boldsymbol{35}\) packages and \(\boldsymbol{20}\) letters in the outgoing mail.

Final Answers

a. The completed two - way frequency table is as shown above.
b. The correct option is A. Letters are delivered less frequently than packages based on the office’s outgoing mail. There are a total of \(\boldsymbol{35}\) packages and \(\boldsymbol{20}\) letters in the outgoing mail.

Answer:

Part a: Completing the Two - Way Frequency Table

Step 1: Find the number of regular letters

We know that for letters, the total number of letters is the sum of regular and overnight letters. Let the number of regular letters be \(x\). We have the equation \(x + 5=20\) (from the total for letters in the completed table). Solving for \(x\), we subtract 5 from both sides: \(x=20 - 5=15\).

Step 2: Find the number of overnight packages

For packages, the total number of packages is the sum of regular and overnight packages. Let the number of overnight packages be \(y\). We know that the total number of packages is 35 and the number of regular packages is 25. So, \(25 + y=35\). Subtracting 25 from both sides, we get \(y = 35-25 = 10\).

Step 3: Find the total number of regular deliveries

The total number of regular deliveries is the sum of regular letters and regular packages. So, \(15+25 = 40\).

Step 4: Find the total number of overnight deliveries

The total number of overnight deliveries is the sum of overnight letters and overnight packages. So, \(5 + 10=15\).
The completed table is:

Type	Regular	Overnight	Total
Package	25	10	35
Total	40	15	55

Part b: Determining the Less Frequent Mail Type

Step 1: Compare the total number of letters and packages

From the table, the total number of letters is 20 and the total number of packages is 35. Since \(20<35\), letters are delivered less frequently than packages.

Step 2: Fill in the blanks

There are a total of 35 packages and 20 letters in the outgoing mail. So the correct option is A. Letters are delivered less frequently than packages based on the office’s outgoing mail. There are a total of \(\boldsymbol{35}\) packages and \(\boldsymbol{20}\) letters in the outgoing mail.

Final Answers

a. The completed two - way frequency table is as shown above.
b. The correct option is A. Letters are delivered less frequently than packages based on the office’s outgoing mail. There are a total of \(\boldsymbol{35}\) packages and \(\boldsymbol{20}\) letters in the outgoing mail.