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

USING METHODS FROM THIS WEEK ABOUT THE BINOMIAL DISTRIBUTION:

a) Find the probability all three residents in the sample are overweight. P(X=3) = ? Would this be unusual?

b) Find the probability none of the three residents in the sample are overweight. P(X=0)= ? Would this be unusual?

c) Use your answers above to fill in this table. You may find it helpful to write your answers in this table.

d) Graph (paper and pencil are great) the probability distribution of X (X on x-axis and probability on the y-axis). Even if you can't show the graph in your hw, do it on scratch paper

e) Find the E(X) = and Var (x) = ² using what you learned about a binomial mean and variance.

f) Find P(more than 1 out of 3 is overweight).

g) Find P(1 or more is overweight). Explain the difference between f and g.