Question

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 ​$25 for the ace of clubs. Find the standard deviation of the amount you might win drawing a card. The standard deviation is ​$nothing .

Answer 1

GIVEN THAT :-

According to the question we have that ,

* If you get a​ spade, you win ​$5

**For any​ club, you win ​$10 plus an extra ​$25 for the ace of clubs.

*** If you get a red​ card, you win nothing.

now

TO FIND :-. Find the standard deviation of the amount you might win drawing a card. The standard deviation is ​$nothing .

now P(X)= 26/52 for red card

=13/52 for spade card

= 12/52 for club (not ace)

= 1/52 club ace

finding the expected amount of winning

for finding the expected amount we have aformula

E(X)=sum of XiPi

substituting the values we get

E(X)=0(26/52)+5(13/52)+10(12/52)+15(1/52)

calculating we get the value as

E(X)=3.846

no calculating variance(X)=E(X^2)-[E(X)]^2

E(X^2)=33.654 ; [E(X)]^2=(3.846)^2

therefore we have that var (X)=18.862

now finding the standared deviation

the formula for the standared deviation is

sqrt of variance

=sqrt of 18.862

= 4.343

there fore ,

the standard deviation of the amount you might win drawing a card. The standard deviation is ​$nothing .=4.343

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