4
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 $1 wager on red. Here's the
probability distribution of X along with summary statistics:
A piz
size
Xro
prot
Lose
Win
-1
1
X = gain ($)
P(X)
20/38
X
18/38
px - $0.05
Mean:
P
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.
The
What are the mean and standard deviation of Z?
any
prot
on a
μ28
dollars
Wha
dollars
Uy