To solve this problem, we need to calculate the relative frequencies of each crashworthiness rating category. The relative frequency is the proportion of cars in each category, which is found by dividing the frequency of each category by the total number of cars.

Part (a): Relative Frequency Distribution

Step 1: Calculate the Total Number of Cars

The total number of cars can be calculated by adding the frequencies of all categories: $\text{Total cars} = 1 + 10 + 3 + 2 = 16$

Step 2: Calculate Relative Frequency for Each Rating

The formula for relative frequency is: $\text{Relative Frequency} = \frac{\text{Frequency of each category}}{\text{Total number of cars}}$

• Good (3): $\text{Relative Frequency} = \frac{1}{16} = 0.0625$

• Acceptable (2): $\text{Relative Frequency} = \frac{10}{16} = 0.6250$

• Marginal (1): $\text{Relative Frequency} = \frac{3}{16} = 0.1875$

• Poor (0): $\text{Relative Frequency} = \frac{2}{16} = 0.1250$

Part (b): Relative Frequency of "Marginal or Worse"

The crash test rating of "Marginal or worse" includes both Marginal (1) and Poor (0) ratings. We need to sum the relative frequencies of these two categories:

$\text{Relative Frequency of Marginal or Worse} = 0.1875 + 0.1250 = 0.3125$

Final Answers

(a) The relative frequency distribution:

• Good (3): $0.0625$
• Acceptable (2): $0.6250$
• Marginal (1): $0.1875$
• Poor (0): $0.1250$

(b) The relative frequency that a randomly selected car will have a crash test rating of "Marginal or worse": $0.3125$

Let me know if you want further details or have any questions!

Here are 5 related questions to further your understanding:

1. How is relative frequency used in probability?
2. How would you interpret the meaning of a rating of "Acceptable" in this context?
3. What other statistics could we calculate from this data, such as the mode or median?
4. How does increasing the total number of cars affect the relative frequency distribution?
5. Can you think of situations where calculating cumulative relative frequency might be useful?

Tip: Always ensure that relative frequencies sum up to 1 to verify your calculations.