Question

below is a table showing the results of a simple random sample asking respondents what types of cars they drive and their commuting distance to work in miles.

car size	commuting distance < 20 miles	commuting distance ≥ 20 miles	total
compact	44	17	61
mid - size	66	33	99
full - size	32	6	38
total	175	75	250

the fraction of drivers who commute at least 20 miles that drive midsize cars is ______.

options:

• 66/99
• 66/175
• 33/75
• 33/99

Explanation:

Step1: Identify relevant counts

We need the number of drivers who commute at least 20 miles (≥20 miles) and drive midsize cars, and the total number of drivers who commute at least 20 miles. From the table, the number of drivers who commute ≥20 miles and drive midsize cars is 33. The total number of drivers who commute ≥20 miles is 75 (from the "Total" row under "≥20 miles" column? Wait, no, wait. Wait, the "Total" for "≥20 miles" is 75? Wait, no, looking at the table: the "≥20 miles" row has totals? Wait, the table has columns: Car size (Subcompact, Compact, Mid - size, Full - size, Total) and rows: Commuting distance (<20 miles, ≥20 miles, Total). Wait, the "≥20 miles" row: Mid - size car has 33, and the total for "≥20 miles" is 75 (since the "Total" column for "≥20 miles" is 75). Wait, no, the "Total" for "≥20 miles" is 75? Wait, the "Total" row for "≥20 miles" is 75? Wait, the table's "≥20 miles" row: Subcompact:19, Compact:17, Mid - size:33, Full - size:6, Total:19 + 17+33 + 6=75. And the number of drivers who commute ≥20 miles and drive midsize cars is 33. Wait, no, the question is "the fraction of drivers who commute at least 20 miles that drive midsize cars". So it's (number of drivers with ≥20 miles and midsize cars) / (number of drivers with ≥20 miles). So numerator: 33 (midsize, ≥20 miles), denominator: total ≥20 miles, which is 75? Wait, no, wait the options: 33/75 is an option. Wait, let's check again. The "≥20 miles" row: Mid - size is 33, and the total for "≥20 miles" is 75 (19 + 17+33 + 6 = 75). So the fraction is 33/75.

Step2: Verify the fraction

So the number of favorable cases (≥20 miles, midsize) is 33, the total number of cases (≥20 miles) is 75. So the fraction is 33/75.

Answer:

33/75