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Math Help - Identifying the type of distribution in each problem

  1. #1
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    Identifying the type of distribution in each problem

    We're going over probability distributions, and I don't have any actual work that I need checked; I want to do these on my own. However I want to make sure I'm on the right track, so for these problems can you let me know that I'm using the right probability distribution?

    And just to be clear, the distributions we're dealing with are binomial, hypergeometric, negative binomial and poisson. There's also A "geo" distribution given, which I assume is geometric, but I've never dealt with that one, so if that's it, please let me know.

    1) A phone operator handles on average 5 calls every 3 minutes. What is the probability that there will be no calls in the next minute?

    This one kind of threw me off because I'm not sure how to derive the probability for a call in any particular minute, but I'm guessing that if I had that it would be a negative binomial distribution?

    2) A fair coin is tossed 10 times. How likely is it to get more than 7 heads?

    The sum of a the binomial distribution for 8, 9, and 10

    3) A typist makes one error in every 500 words. A typical page contains 300 words. What is the probability that there will be no more than two errors in five pages?

    I'm having the same issue with this one that I'm having with the first one. I know I need the probability for error on the page, but I don't know how to get it. I would say that the probability that there's an error on a page is 300/500 = .6, so then the probability that there's no more than two errors would be some function of five pages = 1500 words with a probability of .6 per page, which means .4 that there's no error, so it would be the summation of a binomial distribution for x = 0, 1, 2 with a p of .6 and sample size of 5?

    4) Team A plays team B in a sports game 7 times. The chance that A wins is .6. What is the probability that the series ends after 6 games?

    I was going off of the assumption that this is a negative binomial distribution where I would sum the chance that A wins (B fails) 2 times with the chance that B wins (A fails) 2 times

    5) The probability that a baseball plater gets a hit is .3. What is the probability that he will require five times at bat before his first hit?

    Negative binomial where the chance of not getting a hit .7 and we're looking for r=4 successes?

    Thanks in advance for any help.
    Last edited by Open that Hampster!; March 2nd 2011 at 07:13 PM.
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  2. #2
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    1) No, Binomial has finite limits. Try Poisson with lambda = 5/3.
    2) Good, except "Binomial" is an insufficient description. N = 10 and p = 0.50
    3) Okay, but please specify the SPECIFIC distribution.
    4) No. Negative binomial is not finite. This one MUST end at 7. It's not quite just Binomial, either. Why? Actually, it might be, but I think that's just because the problem statement is worded badly.
    5) Good.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    1) No, Binomial has finite limits. Try Poisson with lambda = 5/3.
    2) Good, except "Binomial" is an insufficient description. N = 10 and p = 0.50
    3) Okay, but please specify the SPECIFIC distribution.
    4) No. Negative binomial is not finite. This one MUST end at 7. It's not quite just Binomial, either. Why? Actually, it might be, but I think that's just because the problem statement is worded badly.
    5) Good.
    1) Thanks. I wasn't sure about that. And I'm assuming x = 0?
    2) Sorry about that, I should have been clearer.
    3) This one I'm still a little stuck on because I'm not sure which binomial distribution it would fit under. Assuming my p = 0.6 is the correct probability for an error on the page, I did the following: (.4)^5 + (.6)*(.4)^4 + (.4)^2*(.6)^3, which intuitively made sense to me as being "the probability that there's no errors in five pages plus the probability that there's 1....) but I don't think that's entirely correct. I just can't put my finger on why I don't think it's correct (other than not knowing which distribution to use)
    4) So you're saying it would be a binomial distribution? I was unaware that negative binomial was finite, but I thought the way I did it sort of flubbed that fact anyway. If I used a binomial distribution, that wouldn't count for cases where there are 6 games played, but A wins the first four (i.e. it ends at 4 instead of 6), so it could be "effectively" a nb

    Thanks for the help so far.
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  4. #4
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    Read that again about the Negative Binomial. It does NOT have a finite Domain.

    IF the teams promise to play all seven games, then it's binomial.
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  5. #5
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    3) Think Poisson.
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