Section 4.4  Means and Standard Deviations of Random Variables
1.In a column bet at roulette, the player bets on twelve numbers.
The chance you win
this bet is 12 out of 38, about
31.6%.
This bet pays 2 to 1.
That means that if you bet
$10 on a column and win, they give you back your $10 plus another $20.
So if you win
you gain $20.
If you lose, you lose your $10, for a gain of
!
$10.
Here is the distribution of the gain for this bet:
net gain
chance
$20
31.6%
!
$10
68.4%
Find the mean and standard deviation of the gain from this bet.
2.
Another Roulette bet is a bet on four numbers. This bet pays 8 to 1, so if you bet
$10 and win you gain $80.
Again, if you lose, your gain is
!
$10.
a.
Find the chance you win and the chance you lose this bet.
b. Write down the distribution of your gain.
c.
Find the mean and standard deviation of your gain.
3.
In the casino game of Keno, 20 balls are picked at random from a collection of 80
balls, numbered 1 through 80.
If you bet on one number (for example, the number 37)
your chance to win is 20 out of 80, or 25%.
This bet pays 2 to 1, so if you bet $10 and
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 Spring '08
 Staff
 Statistics, Probability, Standard Deviation, $1, California Lottery, California Lottery.

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