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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.