How did x>8.3 end up having to be x=8.804?
Oh, now I get the question! If the mean was 8.3, and 20% were considered oversized, and the maximum size for the books 8.9 cm, and normally distributed, that means that 20% are in the topmost range out of all the values, or 40% above the mean...
Wait a second...
Doesn't that mean that the answer is really 8.66 cm? (8.9-(.6*.4))
Or am I missing something?
Or am I just being an idiot?
Thickness of Library Books: The average thickness of books on a library shelf is 8.3 centimeters. The Standard Deviation is 0.6 centimeter. If 20% of the books are oversized,
find the minimum thickness of the oversized books on the library shelf. Assume that the variable is normally distributed.
- Since the question asks what the minimum thickness of oversized books are, we can assume that on the bell
curve the question is asking for the shaded area shown below:
- Now it asks what is the minimum thickness of the book, so that has to be the z-score of the left border of the
shaded area shown.
- Since the shaded area does not intersect with the median, we have to take the value of 20% and subtract it
from the whole value of 50% of the right side of the bell curve, or:
0.5000-0.2000 = 0.3000 which represents the area from the left border of the shaded area to the median.
- This will be what we need to find the z score.
- Using the Standard Normal Distribution Table, we find that there is no exact value for 0.3000. It's comes to a
choice between 0.2995 and 0.3023 making the z score fall at either 0.84 or 0.85.
- Since the value of 0.2995 is the closest, we are able to approximate the z score to be 0.84.
- Now that we have all the information that we need, we now use the formula Z x Standard Deviation + Mean or:
0.84x0.6+8.3=8.804.
- 8.804 being the value of the z score of 0.84 which is the minimum thickness of a book on the library shelf
represented in the shaded area.
Simple, yes? The wording is important and can screw some people up. I also should have mentioned the need for a Standard Distribution table to find some values. So no, you're not an idiot or something, I was negligent in including all the needed information to solve it. But Statistics students would know this without me mentioning it, which is why I didn't since I'm used to helping people understand it in my class. My bad. :)
