You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $10 for the ace of clubs. Find the standard deviation of the amount you might win drawing a card.

Standard deviation = 0.547

Step-by-step explanation:

Given the data

$5 for spade

$10 for any club

$20 for an ace club

Lets assume Probability of getting these cards to be

0.5, 0.20 and 0.30

Therefore, mean would be

Summation (PX) = 5×0.5 + 10×0.2 +20×0.3

Summation (PX)/n= 10.5/35 = 0.3

Standard deviation = √0.3

Standard deviation = 0.547

4.6

Step-by-step explanation:

Let x represent the amount you can win

Therefore

X = (0, 5, 10, 20)

Given that

No. Of red card in a deck = 26

No. Of spade in a deck = 13

No. Of clubs in a deck less ace = 12

No. Of ace in of club = 1

Total number of cards in a deck = 52

Therefore

P(X=0) = P(probability of picking a red card) = 26/52 = 0.50

P(X=5) = P(probability of picking a spade) = 13/52 = 0.25

P(X=10) = P(proability of picking a club, but not the ace) = 12/52 ≈ 0.231

P(X=20) = P(probability of picking the ace of clubs) = 1/52 ≈ 0.019

Next, we find the expected winnings

Recall that,

Expected winnings = mean = μ = E[X] = ∑X × P(X=x)

Therefore,

μ = (0 × 26/52) + (5 × 13/52) + (10 × 12/52) + (20 × 1/52)

μ = 0 + 65/52 + 120/52 + 20/52

= 205/52

= 3.94

Finally, we find the standard deviation

Recall that,

Standard Deviation = Squareroot of the variance = σ

Variance (σ2)= V[X] = ∑X(x−μ)^2 × P(X = x)

σ2=(0−205/52)^2 × (26/52)+(5−205/52)^2 × (13/52) + (10−205/52)^2 × (12/52)+(20−205/52)^2 × (1/52)

σ2 = 42,025/5,408 + 3,025/10,816 + 297,675/35,152 + 697,225/140,608

σ2 = 87,075/10,816 + 145,225/10,816 = 232,300/10,816 = 58,075/2,704 ≈ 21.477

Thus, variance = 21.477

Therefore,

Standard Deviation = squareroot of variance

= Sqroot 21.477

= 4.6

where is the shape my dude?

step-by-step explanation:

squares, rhombus, rectangles