Question

the ages and masses of vehicles of drivers who received speeding tickets in the past 30 days is shown in the table below. use this information to answer parts a through c.

age groups	under 1500 kg	over 1500 kg
26 - 35	190	173
36 - 45	154	160
46 - 55	80	82
>= 56	124	161

(a) construct a relative frequency distribution of the drivers with vehicles under 1500 kg who received tickets.
(round to three decimal places as needed.)

age group	relative frequency
26-35
36-45
46-55
>= 56

Explanation:

Step1: Calculate total frequency for under 1500 kg

First, we sum up the frequencies for the "under 1500 kg" column.
The frequencies are 269 (16 - 25), 190 (26 - 35), 154 (36 - 45), 80 (46 - 55), and 124 (>= 56).
So total frequency \( N = 269 + 190 + 154 + 80 + 124 \)
\( N = 269 + 190 = 459 \); \( 459 + 154 = 613 \); \( 613 + 80 = 693 \); \( 693 + 124 = 817 \)

Step2: Calculate relative frequency for 16 - 25

Relative frequency for a class is \( \frac{\text{Frequency of the class}}{\text{Total frequency}} \)
For 16 - 25: \( \frac{269}{817} \approx 0.329 \) (rounded to three decimal places)

Step3: Calculate relative frequency for 26 - 35

For 26 - 35: \( \frac{190}{817} \approx 0.233 \) (rounded to three decimal places)

Step4: Calculate relative frequency for 36 - 45

For 36 - 45: \( \frac{154}{817} \approx 0.188 \) (rounded to three decimal places)

Step5: Calculate relative frequency for 46 - 55

For 46 - 55: \( \frac{80}{817} \approx 0.098 \) (rounded to three decimal places)

Step6: Calculate relative frequency for >= 56

For >= 56: \( \frac{124}{817} \approx 0.152 \) (rounded to three decimal places)

Answer:

Age Group	Relative Frequency
26 - 35	0.233
36 - 45	0.188
46 - 55	0.098
>= 56	0.152