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Homework Help: Calculate the expected frequencies of 3,4,5 and 6 eggs

  1. Dec 30, 2005 #1
    Hello, i found one question really difficult and I cant solve it. Please help.

    Six hens are observed over a period of 20 days and the number of eggs laid each day is summarised in the following table:

    No. of eggs: 3 4 5 6
    No. of days: 2 2 10 6

    This can be considered as a binomial model, with n=6, for the total number of eggs laid in a day. State the probability that a randomly chosen hen lays an egg on a given day. Calculate the expected frequencies of 3,4,5 and 6 eggs.

    I know the probability required is 5/6. but i dont know how to find the expected frequencies.
  2. jcsd
  3. Dec 30, 2005 #2


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    You said it is a binomial distribution so the frequencies (probabilities) are

    [tex]p_j = \binom {6}{j} \left( \frac {5}{6} \right)^j \left( \frac {1}{6} \right)^{6-j}[/tex]
  4. Dec 30, 2005 #3


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    Tide, that's assuming the base probability is 5/6 which is one of the things Clari needs to determine.

    Clari, you should know that the expected value for a binomial distribution with base probability p is np. The 6 chickens laid a total of 100 eggs in 20 days or an average of 5 eggs per day. Assuming that the sample does reflect the actual expected value, np= 6p= 5 so p= 5/6.

    Now use Tides's suggestion to answer the rest of the problem.
  5. Dec 30, 2005 #4
    Thanks for your help,Tide and HallsofIvy ^-^
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