The following table shows crashworthiness ratings for 16 cars. (3 = Good, 2 = Acceptable, 1 = Marginal, 0 = Poor)

Frontal Crash Test Rating

3

2

1

0

Frequency

1

10

3

2

(a) Find the relative frequency distribution for the experiment of choosing a car at random and determining its frontal crash rating. (Enter your answers to four decimal places.)

Good (3)

Acceptable (2)

Marginal (1)

Poor (0)

(b) What is the relative frequency that a randomly selected car will have a crash test rating of "Marginal" or worse? (Enter your answer to four decimal places.)

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.

The following table shows crashworthiness ratings for 16 cars. (3 = Good, 2 = Acceptable, 1 = Marginal, 0 = Poor)

Frontal Crash Test Rating

3

2

1

0

Frequency

1

10

3

2

(a) Find the relative frequency distribution for the experiment of choosing a car at random and determining its frontal crash rating. (Enter your answers to four decimal places.)

Good (3)

Acceptable (2)

Marginal (1)

Poor (0)

(b) What is the relative frequency that a randomly selected car will have a crash test rating of "Marginal" or worse? (Enter your answer to four decimal places.)

Learn how to calculate the relative frequency distribution for crashworthiness ratings of 16 cars. The problem includes calculating the relative frequencies for Good, Acceptable, Marginal, and Poor ratings and determining the probability of a car having a Marginal or worse crash rating. Suitable for students in Grades 9-12.

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