1.Telephone surveying a group of 200 people to ask if they voted for a candidate.

2.Counting the average number of cats seen at a veterinarian’s office daily.

Look at the experiments described above.

1) Explain why or why these experiments do not represent binomial experiments.

Yes, the only two possible outcomes are that they did, or they didn’t vote for Mr. Bush, so the answer is yes.

No, there are 3 possibilities: red, green, and yellow, so it’s not a binomial experiment.

2) Explain the requirements for a Poisson Distribution and give an example other than one from the text.

In statistics, Poisson distribution is one of the discrete probability distribution.  This distribution is used for calculating the possibilities for an event with the given average rate of value(λ). A Poisson random variable(x) refers to the number of success in a Poisson experiment.

Formula:

  f(x) = e-λλx / x!   Where,   λ is an average rate of value.  x is a Poisson random variable.  e is the base of logarithm(e=2.718).

Example:

   Consider, in an office 2 customers arrived today. Calculate the possibilities for exactly 3 customers to be arrived on tomorrow.

  Step1: Find e-λ.  where,λ=2 and e=2.718    e-λ = (2.718)-2 = 0.135.

  Step2: Find λx.

  where, λ=2 and x=3.  λx = 23 = 8.

  Step3: Find f(x).  f(x) = e-λλx / x!  f(3) = (0.135)(8) / 3! = 0.18.

  Hence there are 18% possibilities for 3 customers to be arrived on tomorrow.

3) How can the Poisson Distribution be used as an approximation for the Binomial Distribution?

When n is large and p is very small, the Poisson distribution can be used to approximate the binomial distribution. The larger the n and the smaller the p, the better is the approximation.