Question

a random sample of packages that were delivered by a company showed that 40% of packages were delayed. the data also showed that 35% of the packages that were on time were out-of-state, while 10% of packages that were delayed were in-state. based on the given information, which of the following relative frequency tables can be constructed?

Explanation:

Identify the given marginal and conditional percentages

$$
LATEXBLOCK0
$$

Calculate the joint relative frequencies

$$
LATEXBLOCK1
$$

Determine the marginal totals for location and match the table

$$
LATEXBLOCK2
$$

The calculated values match the fourth table option (marked with the blue selection dot):

• Delayed & In-State: \(4\%\)
• Delayed & Out-of-State: \(36\%\)
• Delayed Total: \(40\%\)
• On Time & In-State: \(39\%\)
• On Time & Out-of-State: \(21\%\)
• On Time Total: \(60\%\)
• In-State Total: \(43\%\)
• Out-of-State Total: \(57\%\)
• Grand Total: \(100\%\)

Answer:

• (A) Table with: Delayed In-State 30%, Delayed Out-of-State 10%, Delayed Total 40%; On Time In-State 35%, On Time Out-of-State 25%, On Time Total 60%
• (B) Table with: Delayed In-State 10%, Delayed Out-of-State 30%, Delayed Total 40%; On Time In-State 25%, On Time Out-of-State 35%, On Time Total 60%
• (C) Table with: Delayed In-State 36%, Delayed Out-of-State 4%, Delayed Total 40%; On Time In-State 21%, On Time Out-of-State 39%, On Time Total 60%
• (D) Table with: Delayed In-State 4%, Delayed Out-of-State 36%, Delayed Total 40%; On Time In-State 39%, On Time Out-of-State 21%, On Time Total 60% (Correct answer)