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.
- Find the probability all three residents in the sample
are overweight (Find P(X=3) ).
- Find the probability none of the three residents in the
sample are overweight (Find P(X=0) ).
- What are the valid values for X?
- 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.
- Find the probability of each arrangement. (They are not
all equally likely) and check that the probabilities add to
- Find the P(X=0), P(X=1), P(X=2), P(X=3) using your
- Graph the probability distribution of X. (X on x axis
and Probability on the y axis).
- Find the E(X).