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Probability poser

  1. Jun 14, 2009 #1
    A certain type of seed has a probability of 0.8 of germinating. In a pack of 100 seeds, what is the probability that at least 75% will germinate?




    Solution can be achieved on a calculator using binomial theorem. Is there any other way of doing it without using binomial theorem ?
     
  2. jcsd
  3. Jun 14, 2009 #2

    HallsofIvy

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    You could use the normal distribution approximation, with "half- integer correction".

    A binomial distribution in which the probability of a single success is p, repeated n times, has mean [itex]\mu= np[/itex] and standard deviation [itex]\sigma= \sqrt{np(1-p)}[/itex]. If n is large, the normal distribution with the same mean and standard deviation is a good approximation.

    Since a normal distribution allows real number values while a binomial distribution requires integers, you interpret any real number that rounds to a particular integer as being that integer. Here, "at least 75%" or "at least 75 out of 100" would be equivalent to "74.5 or larger". That's the "half integer correction".
     
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