OK. USUALLY when they give you this kind of graph (histogram), each bar tells you the NUMBER of individuals that fall into that particular range.
This graph is a little bit different ... it's easier. On this graph, they're showing you the PROBABILITY that an individual is in that particular range. (The y-axis is labeled 'P', and they told us it's a "probability distribution".)
The graph is telling us that if you close your eyes and pick one giraffe, he has a 25% chance of being 4 years old or younger, a 10% chance of being between 4 and 8, a 35% chance of being between 8 and 12, and a 5% chance of being between 16 and 20.
This is just a fancy, slightly confusing way of saying that 25% of the giraffes in that zoo are 4 or younger, 10% of them are between 4 and 8, 35% of them are between 8 and 12, and 5% of them are between 16 and 20.
Before we worry about answering the question, we can spot a few interesting things about the giraffe population at that zoo:
-- There are NONE that are between 12 and 16 years old. Weird.
-- The percentages only add up to 75%. So 25% of the giraffes must be older than 20 ! They're just not included on the graph.
OK. So the question asks: What's the probability that a giraffe you pick is between 8 and 20 ?
-- He's got a 35% chance of being between 8 and 12, no chance at all of being between 12 and 16, and a 5% chance of being between 16 and 20.
Can you see that his chance of being between 8 and 20 is
No. This is because the y value of 1 repeats itself, which never happens in an exponential function. This function is likely quadratic, which forms a parabola.
