Machine Juice Liquid
probability question! Will rate best answer!?
1.One thousand independent rolls of a fair die will be made. computer an approximation to the probability that the number 6 will appear between 150 and 200 times inclusive.
i got: 0.9528
2.A company that manufactures and bottles apple juice uses a machine that automatically fills 16-ounce bottles. There is some variation, however, in the amount of liquid dispensed normally distributed with mean 16 ounces and standard deviation 1 ounce.What proportions of bottles will have more than 17 ounces dispensed into them?
I got: 0.3413
please help with either question! Your help is appreciated and i will rate best answer! If i got it wrong please show me how you did your answer so i can learn from my mistakes?
Problem 1
I used the binomial probability function on Excel.
I set up cells A through A51 to run from 150 to 200. In column B1 I typed
=BINOMDIST(A1,1000,0.16666666667,FALSE)
into the formula bar and copied it all the way down to B51
I summed up the separate probabilities and got .926453
Problem 2
You need to convert this to the standard normal value of z.
The formula is:
z = (x - µ)/σ
z = (17 - 16)/1 = 1/1 = 1.0
You need to look up the value of z in a Standard Normal Table to find the probability that a bottle will fall into the right tail of the curve above z = 1.00
You very likely have a z curve in your text book but I like to use:
http://lilt.ilstu.edu/dasacke/eco148/ztable.htm
and I find that at z = 1.00, the number in the table is .8413
This table show the area BELOW a given z value but, since you want to know the proportion of bottles that have more than 17 oz, you need to know the value ABOVE the z value.
You can get that by using the complement rule:
1 - ,8413 = .1587
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bottle cup filling machine water yoghurt www.cemremakina.com
Liquid Calories- How They Affect Weight Loss
If you think you know exactly how the liquids you consume affect your weight loss effort, you probably don't really know as much as you think. The advice to drink '8 glasses of water a day' or to switch regular soda with diet, is probably not new to you. But is that really all we need to be doing, and is that really even good advice? The answers may surprise you.
First lets start with those eight glasses of H2O that we all know we need. That age old advice is spot on, but don't gulp those eight glasses down all at once. And you shouldn't be leaving those servings to mealtime. Of course, if you must do these two things, it's better than not getting your daily requirement. But to keep your metabolism working at it's best, get yourself a large thermos and sip your water throughout the day. Think of your body as a machine- if you oil that machine all at once, yes, it will work. But wouldn't it be more efficient if you slowly oiled it throughout the day? It sure would. Better yet, make sure your water is freezing cold. It will not only be more refreshing, but your body will also use more calories just warming the water up.
But what is a few extra calories, right? Actually, if warming up that water burns twenty extra calories a day, that will come out to you losing over two pounds a year. Just for drinking your water cold as can be. If two pounds a year doesn't sound like much to you- I'm sure a twenty-one pound weight loss in ten years sound better. I surely don't want to gain twenty-one pounds in the next ten years. And I bet you don't either.
In addition, it is best not to drink anything with your meals. Obviously, this is against the habits of most, yet aids with digestion. Consuming liquids during a meal dilutes stomach acid, therefore making it harder for your body to digest your food. To further aid digestion- chew your food as well as you can, so it's broken down into almost a liquid form and much easier to digest. This has to do with weight loss, because the more efficiently your body works as a whole- the faster and less of a struggle it will be to lose weight.
On to my next topic, soda and diet soda. It angers me when I browse a diet plan and I see that one fruit juice a day is permitted, but 'as much diet soda as you'd like' is also allowed. I really don't want to inundate you with the ingredients in diet soda, but to say it plainly, they basically contain chemicals. As dramatic as this sounds, there are studies linking Aspartame to cancer. Not only that, but soda and carbonation in general will inhibit your body's absorption of calcium and is also dehydrating. Dehydrated skin leads to bloated, older looking skin, which is not exactly optimal. Another fun fact about Aspartame is that it causes more food cravings. As your body get's ready for the sugar that never comes, it trigger even more cravings to satisfy the hunger for the sugar that didn't come. Gee, just what dieters need.. why is this considered a 'diet' drink again?
Also, allow me to clarify, I am not advocating that anyone should switch back to regular soda. Coca Cola can take the paint right off of a car. I would not put that in MY body, as I surely don't want anyone else putting it in theirs. If you really feel the urge to drink something soda-like you can be a bit more healthy and mix some 100% natural fruit juice with some soda water. Just remember to take those calories into consideration once you hit the gym or add up your calories for the day.
Or opt for some tea. Studies have shown that consuming 3-4 cups of green tea a day can help burn up to 50 more calories. Again, that doesn't sound like a huge amount, but it comes out to almost half a pound a month, and 6 pounds in one year. And it takes almost no effort... who doesn't like easy?
Some other teas I enjoy are yerba mate, which contains about 1/3 the amount of caffeine as a cup of coffee and Oolong Tea. Oolong tea is a Chinese tea and besides it's cool name is known for it's weight loss properties. Buy organic if you can (though you should ALWAYS get organic if you can).
Alcoholic drinks are also a dieters nightmare. As depressing as it is, too much party equals not enough weight loss. Some mixed drinks have an enormous amount of calories. So much so that you are basically drinking your dessert (and then some). Which is obviously not conducive to weight loss. Though I don't want to ruin your next boozing adventure, you should know that a regular margarita ordered in a restaurant can easily have up to 700 calories. So stick to light beer and wine, but keep in mind, the sweeter the wine, the higher the calories.
For another totally fun-killing fact: After consuming two standard alcoholic drinks, you're body burns 73% less fat. The main energy source your body metabolizes becomes alcohol, so better to avoid fattening foods while drinking, as your body will store the fat. And no, three shots each in two rum-and-diets does not constitute as two standard drinks. But obviously you aren't drinking diet soda- you know better.
While the majority of this information is not what most want to hear, liquid calories are very important to consider while striving for your weight loss goals.
About the Author
Katie has an active interest in weight loss and nutrition and hopes to help women lose weight and live healthy, happy lives. You can follow her research at:
