According to gregmat’s video the middle value will divide the area into two equal halves, even though the middle value will be closer to the mean value. SO both A and B should be equal to 34
It’s true that both intervals cover 0.6 grams, but which interval captures more of the middle?
My understanding is that the line in the middle will divide the 34% into equal halves.
Since the areas are equal, the percentages are equal, hence they both capture the same amount
Rewrite the quantities:
Quantity A = (percent of the insects that have a mass between 5.2 and 5.5) + (percent of the intersects that have a mass between 5.5 and 5.8)
Quantity B = 2 \cdot (percent of the intersects between 5.2 and 5.5)
The justification for rewriting Quantity B as follows is that the portion of the distribution’s graph to the left of the mean is a reflection of the portion to the right (across the mean). In other words, because the distribution is symmetric about its mean, (the percentage of insects with a mass between 4.9 and 5.2) = (percentage of insects with a mass between 5.2 and 5.5).
Finally, subtract a copy of (percent of the intersects between 5.2 and 5.5) from both quantities, leaving you with the following:
Quantity A: (percent of the intersects that have a mass between 5.5 and 5.8)
Quantity B: (percent of the intersects that have a mass between 5.2 and 5.5)
I think the final step should likely be obvious now