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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
X = gain (S) -1 1
Р(X) 20/38 18/38
Мean: Ax-$0.05
Standard deviation: ax$1.00
Suppose a player decides to wager $5 instead of winning $5.
Let Z represent the player's gain from a random $5 wager on red. possible outcomes become either losing or , so
What are the mean and standard deviation of Z? dollars?

Sagot :

fichoh

Answer:

-$0.26 ; $5

Step-by-step explanation:

Given that :

____________ Lose ______ Win

X =$1 _______ - $1 ________ $1

P(X) _______20/ 38 _____ 18/38

Mean, Ux = - $0.05

Standard deviation, σx = $1.00

If the wager is $5 instead of $1

Mean = Σx*p(x)

Mean = (-5 * 20/38) + (5 * 18/38)

Mean = - 2.6315789 + 2.3684210

Mean (μ) = −0.26

Standard deviation :

Sqrt(Σx²p(x) - μ²)

[(-5^2)*(20/38) + (5^2)*(18/38)] - (-0.26^2)

(13.157894 + 11.842105) - 0.0676

= 24.999999 - 0.0676

= sqrt(24.932399)

= 4.9932353

= 5

View image fichoh
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