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# Reasonable inferences from estimates

Video transcript
Mary has decided to buy a new car. The local car dealership states the car she is considering has an estimated gas mileage of 24 miles per gallon. The car has a 12 gallon tank. Mary tells her friend that the car will travel exactly 288 miles on a full tank of gas. Is this a reasonable statement? Why or why not? And I encourage you to pause this video now and look at these statements. And think about is this a reasonable statement, yes or no? And then justify. Use one of these justifications to say whether it is a reasonable statement or not. So let's read through each of them. So the first one says, yes, it is a reasonable statement for Mary to tell her friend that the car will travel exactly 288 miles on a full tank of gas. And the rationale is, the car can travel exactly 24 miles per gallon times 12 gallons. We see that the units, the gallon in the numerator, gallon in the denominator cancel out. And we're left with 24 times 12, which is 288. And the units we're left with is miles. 288 miles on 1 tank of gas. Now there's one little thing that makes this-- the math seems right. The unit cancellation seems right, the dimensional analysis, so to speak. But it seems like the statement is using a stronger assumption than what the car dealer told her. The car dealer told her that it has an estimated gas mileage of 24 miles per gallon. To do this, she would have to assume that the car can travel exactly 24 miles in a gallon. There's a big difference between an estimate and being exactly 24 miles per gallon. In the estimate, first of all, they might have rounded it. When they did the tests, it might have been 23.9. It might have even have been 23.6 miles per gallon. Or it might have been 24.4 miles per gallon. That's a pretty big difference. You definitely wouldn't get to exactly 288 miles. The other thing is this estimate is probably based on an average of traveling many, many, many miles in different conditions. You get better gas mileage if you're on the highway, or if you're going downhill. And you get worse gas mileage if you're in traffic, or if you're going uphill, or if there's a strong headwind. So it just averages here. So you can't say that it's going to go exactly 288 miles without knowing exactly how this was measured. And frankly, every car is going to be a little bit different. The octane of the fuel will be a little bit different. And so that's why it's hard to make this assumption right over here, that the car can travel exactly 24 miles per gallon. The dealership just gave an estimate. So let's go to B. Yes, the estimated gas mileage of the car can be used to calculate the exact distance the car will travel on any one tank of gas. Well, no, we just already said it's an estimate. It's roughly how far the car can travel on a tank of gas, but it's not the exact distance the car will travel on any one tank of gas. C, no, it's not a reasonable statement. 24 miles per gallon is an estimate, likely rounded to the nearest integer, so it would not be reasonable to try to calculate the exact distance the car can travel. That's what I think I've been saying all along throughout this video. So let's just read D. No, the distance the car will travel is found by dividing 24 miles per gallon by 12 gallons. No, this is just wrong. This is wrong mathematically, and this is just troublesome on a lot of levels. C is the right answer. D is the most wrong of all the answers here.