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In a certain county, 27% of the residents are overweight. Choose 3 residents at random. Let...

In a certain county, 27% of the residents are overweight. Choose 3 residents at random. Let X= the number of overweight residents in the sample.

  1. Find the probability all three residents in the sample are overweight (Find P(X=3) ).
  1. Find the probability none of the three residents in the sample are overweight (Find P(X=0) ).
  1. What are the valid values for X?
  1. There are eight possible arrangements for the sample of three where 0=overweight N=not overweight. For example (O,O,O) means all three are overweight. (N,O,O) means that the first person is not overweight but the second and third residents are overweight. List all eight arrangements.

  1. Find the probability of each arrangement. (They are not all equally likely) and check that the probabilities add to one.
  1. Find the P(X=0), P(X=1), P(X=2), P(X=3) using your answers above.
  2. Graph the probability distribution of X. (X on x axis and Probability on the y axis).

  1. Find the E(X).
Math   Statistics-And-Probability   
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