Answer:
Step-by-step explanation:
Given:
Car has three times the utility of its nearest competitor.
Walking has a utility 0.15 points lower than buses.
Buses have an average utility of 0.1 for the route.
Trains' utility is rated twice as high as buses.
To calculate the expected number of people driving, we need the relative utilities of each method of travel. Let's assign variables to represent the utilities:
Car's utility = 3
Nearest competitor's utility = X
Walking's utility = X - 0.15
Bus's utility = 0.1
Train's utility = 2 * 0.1 = 0.2
Now, let's compare the utilities:
Car: 3
Walking: X - 0.15
Bus: 0.1
Train: 0.2
From the given information, we know that the car has three times the utility of its nearest competitor. Therefore, we can set up the equation:
3 = X - 0.15
Solving for X:
X = 3 + 0.15
X = 3.15
Now that we know the nearest competitor's utility (X) is 3.15, we can calculate the probability of choosing the car:
Probability of choosing car = Car's utility / (Car's utility + Nearest competitor's utility + Walking's utility + Bus's utility + Train's utility)
= 3 / (3 + 3.15 + (3.15 - 0.15) + 0.1 + 0.2)
= 3 / 9.45
≈ 0.3175
Finally, we calculate the expected number of people driving:
Expected number of people driving = Probability of choosing car * Total number of people
= 0.3175 * 1000
≈ 317.5
Rounding to the nearest whole number, we would expect approximately 318 people to drive this route on any given day.
Therefore, the closest answer option to the expected number of people driving is 292.