SOLUTION: This is in my text book and I am trying to understand and work out problems 55 and 56. I have struggled for over 3 hours now and am getting nowwhere can you help me please? I k

Question 143683This question is from textbook Mathematics All Around
: This is in my text book and I am trying to understand and work out problems 55 and 56. I have struggled for over 3 hours now and am getting nowwhere can you help me please?
I know you have to draw the bell curve but i do not understand how and where to put the numbers etc. I am drawing a blank here. I know the rule is 68%,95%, 99.7% rule. What little step am i missing? Can you please help turn on the light bulb for me. This is not an assigned problem but i have other like it and need to know how to do them. Any help from you would be a blessing and so appreciated.

Question:
Due to random variations in the operation of an automatic coffee machine, not every cup is filled with the same amount of coffee. Assume that the mean amount of coffee dispernsed is 8 ounces and the standard deviation is 0.5 ounces. Use Figure 14.12 to solve.( Which is just a bell cure showing the 68-95-99.7 rule for normal distribution).
I know the mean is in the middle, after that i just sit here looking at it. Please help.
Problem 55. Analyzing vending machines.
a. What percentage of the cups should have at least 8 ounces of coffee?
b. What percentage of cups should have less than 7.5 ounces of coffee?
How do i draw the curve to obtain this information?
Can you please show/tell me in detail so i can understand? Thank You This question is from textbook Mathematics All Around

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Since the mean is 8 oz, the answer to part a) is HALF. That is, 50%.

For the b) part, you must draw a bell-shaped curve, and mark off three standard deviations to the left and three to the right. Do you know what I mean by this? Then, label the mean in the middle at 8 oz., and to the right, ADD .5 oz for each mark, and to the left SUBTRACT .5 oz. This is what you should have, from left to right:
6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5.

Now, the "area" within 1 standard deviation of the mean represents 68% of the total area, and it is divided with half on each side of the mean. This means that you have 34% of the area on each side. So the number of cups that are LESS THAN 7.5 oz will be 50% - 34%=16%.

If by chance you wanted to know how many are MORE than 7.5 oz, you would have to add 34% + 50%= 84%.

A picture would be worth a thousand of these paragraph explanations, but I don't know how to do draw a bell curve in this medium.

R^2
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