rolling a die

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mexx

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May 21, 2006
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15
exercise:

if the die was rolled sixty times, the expected value for the number of times face 5 shows up would be 10.
calculate the probability that it shows up
a) exactly 10 times
b) 10 +/- 1 times (i.e. between 9 and 11)
c) 10 +/- 2 times
d) 10 +/- 5 times
e) 10 +/- 10 times
which range would guarantee a 90 % certainty? 95 % certainty? 99% certainty?

calculations are necessary. but important is the discussion of the results...

can you help me??
thanks for showing me your calculations, thoughts, ideas, explanations, ...
 
Use the normal distribution approximation to the binomial distribution.
 
we just started, but we didn't get any practical advice to solve this exercise.
the teacher wants us to do it alone... but she will grade this homework..
so couldn't you tell me how i have to calculate the probabilities?
and how i can find out, which ranges would guarantee this given certainties?


greets from bella italia:)
 
mexx said:
...couldn't you tell me how i have to calculate the probabilities?
Click to expand...
Um... the other tutor kinda already did that.... The difficulty here is that we really can't provide the missing classroom instruction. You say that your teacher hasn't covered this, and apparently your book doesn't, either. So you're needing a few hours of one-on-one teaching. But, obviously, we cannot provide that. :oops:

:!: (Mathnerds volunteers can help students work through specific exercises, but this assistance requires that the student have at least some grasp of the underlying concepts and methods, something you indicate is missing. It simply isn't reasonably feasible for us to attempt, within this environment, to provide that foundational underpinning.) :!:

I'm assuming you've already tried reading web lessons on the topic indicated by the tutor, but they didn't help. So you might want to consider hiring a tutor, local to your area, to provide the hours of instruction that your classroom teacher is denying your group. :shock:

My best wishes to you! 8-)

Eliz.
 
ok. thanks so long..

umm, but you could just give me the needed formula and then i'll be able to solve it. even if i don't understand... (that's not what counts in our maths-lesson..)

:roll:

that would be very nice..
 
For b:

Use the binomial and add up the probabilitties from 9 to 11. The others are the same method only use 8 to 12 and so forth.

\(\displaystyle \L\\\sum_{k=9}^{11}C(60,k)(\frac{1}{6})^{k}(\frac{5}{6})^{60-k}=C(60,9)(\frac{1}{6})^{9}(\frac{5}{6})^{51}+C(60,10)(\frac{1}{6})^{10}(\frac{5}{6})^{50}+C(60,11)(\frac{1}{6})^{11}(\frac{5}{6})^{49}=?\)
 
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