Answer:
To find the associated probability distribution, we need to determine the probabilities for each category of vehicles: pickups, passenger cars, SUVs, and minivans.
Given the information provided:
- 5% of all light vehicles sold were pickups, so the probability of selecting a pickup is 0.05.
- 35% of all light vehicles sold were passenger cars, so the probability of selecting a passenger car is 0.35.
- A randomly chosen vehicle sold in 2000 was twice as likely to be an SUV as a minivan. Let's denote the probability of selecting a minivan as "x". Therefore, the probability of selecting an SUV is 2x.
Since the sum of all probabilities should equal 1, we can set up an equation:
0.05 + 0.35 + 2x + x = 1
Combining like terms:
3x + 0.4 = 1
Subtracting 0.4 from both sides:
3x = 0.6
Dividing both sides by 3:
x = 0.2
Now we can determine the probabilities for each category:
- Probability of selecting a pickup: 0.05
- Probability of selecting a passenger car: 0.35
- Probability of selecting an SUV: 2x = 2(0.2) = 0.4
- Probability of selecting a minivan: x = 0.2
Therefore, the associated probability distribution is as follows:
Pickup: 0.05
Passenger Car: 0.35
SUV: 0.4
Minivan: 0.2