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## Main Question or Discussion Point

So, I have been studying for my chemistry quiz and I came across a problem that I can't really get, or rather, part of the solution.

The problem itself is easy, it's just the way my teacher solved what confuses me. Here it is and thanks in advance.

There was an histogram for lightbulbs where <x> (average lifetime) = 845.2 hr and s (standar deviation) = 94.2 hr.

b) What fraction of the bulbs is expected to have a lifetime between 798.1 and 901.7?

So here is how i would approach the problem. Given the Z Distribution table.

Z1 = (x - <x>)/s = (798.1 - 845.2)/94.2 = -0.5 or just 0.5; since the graph is the same on either side of the y axis, the area from 0 to 0.5 and from 0 to -0.5 will be the same.

Z2 = (901.7 - 845.2)/94.2 = 0.6

So i go to the table, and I find that the area from 0 to 0.5 is .1915 and the area from 0 to 0.6 is .2258.

Now here is where i get confused. In order to find the area in between (and eventually the number of bulbs in between 798.1 and 901.7) my professor ADDED the two areas. That blew my mind, I thought you were supposed to substract the area from 0 to 0.5 from the area from 0 to 0.6 to get the area in between... but no, she added them and the book does the same thing but they dont explain why, please any help? I would like to know why the added them Tahnks!

The problem itself is easy, it's just the way my teacher solved what confuses me. Here it is and thanks in advance.

There was an histogram for lightbulbs where <x> (average lifetime) = 845.2 hr and s (standar deviation) = 94.2 hr.

b) What fraction of the bulbs is expected to have a lifetime between 798.1 and 901.7?

So here is how i would approach the problem. Given the Z Distribution table.

Z1 = (x - <x>)/s = (798.1 - 845.2)/94.2 = -0.5 or just 0.5; since the graph is the same on either side of the y axis, the area from 0 to 0.5 and from 0 to -0.5 will be the same.

Z2 = (901.7 - 845.2)/94.2 = 0.6

So i go to the table, and I find that the area from 0 to 0.5 is .1915 and the area from 0 to 0.6 is .2258.

Now here is where i get confused. In order to find the area in between (and eventually the number of bulbs in between 798.1 and 901.7) my professor ADDED the two areas. That blew my mind, I thought you were supposed to substract the area from 0 to 0.5 from the area from 0 to 0.6 to get the area in between... but no, she added them and the book does the same thing but they dont explain why, please any help? I would like to know why the added them Tahnks!