# Probability

Suppose you roll a die. If you roll an odd number, you win the dollar amount corresponding to the number of dots showing. If you roll an even number, you lose the number of dollars corresponding to the number of dots. (For example, if you roll a three you win $3. If you roll a six, you lose $6.) You pay $.50 (fifty cents) to play this game.

a. Find the distribution of the winnings for this game.

b. The amount won is a (discrete, continuous) variable.

c. Find the expected (mean) winnings for this game.

d. Find the standard deviation of the winnings for this game.

e. Suppose you played this game 100 times. Find the mean and standard deviation for the sample mean winnings.

f. The result used in part e. is the ______________________.

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#### Solution Summary

Suppose you roll a die. If you roll an odd number, you win the dollar amount corresponding to the number of dots showing. If you roll an even number, you lose the number of dollars corresponding to the number of dots. (For example, if you roll a three you win $3. If you roll a six, you lose $6.) You pay $.50 (fifty cents) to play this game.

a. Find the distribution of the winnings for this game.

b. The amount won is a (discrete, continuous) variable.

c. Find the expected (mean) winnings for this game.

d. Find the standard deviation of the winnings for this game.

e. Suppose you played this game 100 times. Find the mean and standard deviation for the sample mean winnings.

f. The result used in part e. is the ______________________.