Question

A survey of 3,000 who bought a new car showed that 900 people had

mechanical issues within the first 2 year.
a. What is the relative frequency of the people that had mechanical issues?
b. What is the relative frequency of the people that did not have mechanical
issues?
c. What does the relative frequencies in part (a) and (b) tell you about the
new car and how reliable it has been? Explain your reasoning.

Answer 1

The relative frequency of people who had mechanical issues with their new car is 30%, while the relative frequency of those without issues is 70%. This suggests that a significant portion of the cars might be reliable, but there is still a considerable number of issues.

The relative frequency is calculated as the number of times a particular value occurs relative to the total number of occurrences. In this case, to find the relative frequency of people who had mechanical issues, we divide the number of people with mechanical issues by the total number of people surveyed:

a. The relative frequency of people that had mechanical issues is 900 / 3,000 = 0.3 or 30%.

b. To find the relative frequency of people who did not have mechanical issues, we subtract the number of people with issues from the total and divide that by the total number of people surveyed. This gives us (3,000 - 900) / 3,000 = 2,100 / 3,000 = 0.7 or 70%.

c. The relative frequencies in parts (a) and (b) tell us that in terms of reliability, 30% of new car buyers faced mechanical issues within the first two years, which may suggest moderate reliability issues. Conversely, the majority, or 70%, did not face such issues, indicating a substantial proportion of these cars could be considered reliable over that time frame.

Answer 2

A. The relative frequency of the people that had mechanical issues is 30%.

B. The relative frequency of the people that did not have mechanical issues is 70%.

C. The relative frequencies in (a) and (b) suggest that the new car has been relatively unreliable, as 30% of buyers experienced mechanical issues within the first two years. This suggests that the car has not been built to a high standard of quality, and that buyers should be prepared for potential issues with the car.