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The mass of tea in Supacuppa teabags has a normal distribution with mean 4.1g and standard deviation 0.12 g. The mass of tea in Bumpacuppa teabags has a normal distribution with mean 5.2g and standard deviation 0.15g.
i) Find the probability that a randomly chosen Supacuppa teabag contains more than 4.0 g of tea [SOLVED: normalcdf(4.0,E99,4.1,0.12) = 0.798]
ii) Find the probability that out of two randomly chosen Supacuppa teabags, one contains more than 4.0g of tea and one contains less than 4.0g of tea. [SOLVED: normalcdf(4.0,E99,4.1,0.12) = 0.798, normalcdf(-E99,4.0,4.1,0.12) = 0.202, 0.798*0.202*2=0.323]
iii) Find the probability that five randomly chosen Supacuppa teabags contain a total of 20.8g of tea.
I tried normalcdf(20.8,E99,4.1,0.12), normalcdf(20.8,E99,20.5,0.12) and normalcdf(4.16,E99,4.1,0.12) but none of the three give the correct answer. I just need a hint, what method to use.
iv) Find the probability that the total mass of tea in five randomly chosen Supacuppa teabags is more than the total mass of tea in four randomly chosen Bumpacuppa teabags.
I think once I figure out the method for iii) I can solve this but need your help for iii). If you ask me to do my own homework, note I already solved i) and ii) and my teacher sucks at explaining all these concepts. —Preceding unsigned comment added by 166.121.36.232 ( talk) 09:53, 21 April 2010 (UTC)
The article on the Wronskian gives an example of two examples that are linearly independent with a Wronskian of zero. The second function used is defined as the negative of the first function for negative x's, and first function for positive x's. I was wondering if there was an example of two linearly independent and infinitely differentiable functions that have a Wronskian of zero. I would imagine that the second function would still have to be defined piecewise, with f2(x) = 0 for x<=0 and f2(x) = f1(x) for x>0, but I can't seem to make this second function infinitely differentiable. 173.179.59.66 ( talk) 15:14, 21 April 2010 (UTC)
So I've been looking into precalc/calc math a bit to see how things build upon each other and I've kinda gotten a bit stuck. I've always been told the sine and cosine angle sum formulas without any reason as to why they are true. Progressing through calculus, I have seen their use in the derivations for the derivatives of sine and cosine through the limit definition of the derivative. Knowing those, one can derive the Maclaurin series for the sine and cosine. Rearrangement of the Maclaurin series for gives Euler's formula. Plugging in into Euler's formula can prove the sine and cosine sum formulas. Clearly, we're just going in a circle. Which of these steps came first? How did we know that the derivative of sine is cosine without knowledge of the sine and cosine sum formulas? Or, alternatively, how did we know of the sine and cosine double angle formulas without the knowledge of the derivatives of sine and cosine? All the proofs that I've seen for these two things somehow have either gone back to calculus or gone back to the sum formulas, and I can't seem to find something to prove these concepts with the other known properties of the trig functions. How did these ideas come to be? — Trevor K. — 21:40, 21 April 2010 (UTC) —Preceding unsigned comment added by Yakeyglee ( talk • contribs)
I was fortunate in that in 8th and 9th grades I had a math teacher who was honest, as opposed to one who says "This is important material for you to learn; you'll understand why later" when the instructor saying that does not in fact understand. In 9th grade we went through careful geometric proofs of these identities. I would think those must be much older than calculus; I suspect that Regiomontanus knew these identities. Michael Hardy ( talk) 22:00, 23 April 2010 (UTC)
Mathematics desk | ||
---|---|---|
< April 20 | << Mar | April | May >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
The mass of tea in Supacuppa teabags has a normal distribution with mean 4.1g and standard deviation 0.12 g. The mass of tea in Bumpacuppa teabags has a normal distribution with mean 5.2g and standard deviation 0.15g.
i) Find the probability that a randomly chosen Supacuppa teabag contains more than 4.0 g of tea [SOLVED: normalcdf(4.0,E99,4.1,0.12) = 0.798]
ii) Find the probability that out of two randomly chosen Supacuppa teabags, one contains more than 4.0g of tea and one contains less than 4.0g of tea. [SOLVED: normalcdf(4.0,E99,4.1,0.12) = 0.798, normalcdf(-E99,4.0,4.1,0.12) = 0.202, 0.798*0.202*2=0.323]
iii) Find the probability that five randomly chosen Supacuppa teabags contain a total of 20.8g of tea.
I tried normalcdf(20.8,E99,4.1,0.12), normalcdf(20.8,E99,20.5,0.12) and normalcdf(4.16,E99,4.1,0.12) but none of the three give the correct answer. I just need a hint, what method to use.
iv) Find the probability that the total mass of tea in five randomly chosen Supacuppa teabags is more than the total mass of tea in four randomly chosen Bumpacuppa teabags.
I think once I figure out the method for iii) I can solve this but need your help for iii). If you ask me to do my own homework, note I already solved i) and ii) and my teacher sucks at explaining all these concepts. —Preceding unsigned comment added by 166.121.36.232 ( talk) 09:53, 21 April 2010 (UTC)
The article on the Wronskian gives an example of two examples that are linearly independent with a Wronskian of zero. The second function used is defined as the negative of the first function for negative x's, and first function for positive x's. I was wondering if there was an example of two linearly independent and infinitely differentiable functions that have a Wronskian of zero. I would imagine that the second function would still have to be defined piecewise, with f2(x) = 0 for x<=0 and f2(x) = f1(x) for x>0, but I can't seem to make this second function infinitely differentiable. 173.179.59.66 ( talk) 15:14, 21 April 2010 (UTC)
So I've been looking into precalc/calc math a bit to see how things build upon each other and I've kinda gotten a bit stuck. I've always been told the sine and cosine angle sum formulas without any reason as to why they are true. Progressing through calculus, I have seen their use in the derivations for the derivatives of sine and cosine through the limit definition of the derivative. Knowing those, one can derive the Maclaurin series for the sine and cosine. Rearrangement of the Maclaurin series for gives Euler's formula. Plugging in into Euler's formula can prove the sine and cosine sum formulas. Clearly, we're just going in a circle. Which of these steps came first? How did we know that the derivative of sine is cosine without knowledge of the sine and cosine sum formulas? Or, alternatively, how did we know of the sine and cosine double angle formulas without the knowledge of the derivatives of sine and cosine? All the proofs that I've seen for these two things somehow have either gone back to calculus or gone back to the sum formulas, and I can't seem to find something to prove these concepts with the other known properties of the trig functions. How did these ideas come to be? — Trevor K. — 21:40, 21 April 2010 (UTC) —Preceding unsigned comment added by Yakeyglee ( talk • contribs)
I was fortunate in that in 8th and 9th grades I had a math teacher who was honest, as opposed to one who says "This is important material for you to learn; you'll understand why later" when the instructor saying that does not in fact understand. In 9th grade we went through careful geometric proofs of these identities. I would think those must be much older than calculus; I suspect that Regiomontanus knew these identities. Michael Hardy ( talk) 22:00, 23 April 2010 (UTC)