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A customs agent discovers 22 identically looking packets of white power in a traveler's suitcase. Unknown to the customs officer, 17 of these packets contain

A customs agent discovers 22 identically looking packets of white power in a traveler's suitcase. Unknown to the customs officer, 17 of these packets contain cocaine, the rest do not contain cocaine.

The customs officer is to randomly pick 4 packets and test each one. A random variable X is to count the number of tested packets that test positive for cocaine.

(a) Finish the probability distribution of X below. Use four decimals in each of your entries.

X 0 1 2 3 4

P(X=x)

(b) From the distribution you found in part (a), what can you say about the distribution of X?

The distribution of X is .

(c) How many of the 4 packets do you expect be to test positive for cocaine? Provide the standard deviation as well.

E(X)=

SD(X)=

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