A roulette wheel consists of 18 red slots, 18 black slots, and 2 green slots. A player can wager $1 that a marble will land in a red slot, in which case the player would gain a $1. If the marble lands in a slot that isn't

red, then the player loses their $1 wager. Let X represent the player's gain from a random $1 wager on

red. Here's the probability distribution of X along with summary statistics:

Lose

Win

-1

1

X = gain ($)

P(X)

20/38

18/38

Mean:

ux~-$0.05

Standard deviation:

ox~$1.00

Suppose a player decides to wager $5 instead of $1, so the possible outcomes become either losing or

winning $5. Let Z represent the player's gain from a random $5 wager on red.

What are the mean and standard deviation of Z?