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	190
46 - 55	80	82
>= 56	124	181

(round to three decimal places as needed.)

age group	relative frequency
26-35	0.233
36-45	0.188
46-55	0.098
>= 56	0.162

(b) construct a relative frequency distribution of the drivers with vehicles over 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 number of drivers with vehicles over 1500 kg

First, we sum up the frequencies for "over 1500 kg" across all age groups.
The frequencies are 224 (16 - 25), 173 (26 - 35), 160 (36 - 45), 82 (46 - 55), and 161 (≥ 56).
So total \( N = 224 + 173 + 160 + 82 + 161 \)
\( N = 224 + 173 = 397 \); \( 397 + 160 = 557 \); \( 557 + 82 = 639 \); \( 639 + 161 = 800 \)

Step2: Calculate relative frequency for each age group

For 16 - 25:

Relative Frequency \( = \frac{224}{800} = 0.280 \)

For 26 - 35:

Relative Frequency \( = \frac{173}{800} = 0.21625 \approx 0.216 \) (rounded to three decimal places)

For 36 - 45:

Relative Frequency \( = \frac{160}{800} = 0.200 \)

For 46 - 55:

Relative Frequency \( = \frac{82}{800} = 0.1025 \approx 0.103 \) (rounded to three decimal places)

For ≥ 56:

Relative Frequency \( = \frac{161}{800} = 0.20125 \approx 0.201 \) (rounded to three decimal places)

Answer:

Age Group	Relative Frequency
26 - 35	0.216
36 - 45	0.200
46 - 55	0.103
≥ 56	0.201