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

[Clari]

Hello, i found one question really difficult and I can't 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 don't know how to find the expected frequencies.

 

[Tide]

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

$$p_j = \binom {6}{j} \left( \frac {5}{6} \right)^j \left( \frac {1}{6} \right)^{6-j}$$

 

[HallsofIvy]

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.

 

[Clari]

Thanks for your help,Tide and HallsofIvy ^-^