SOLUTION: I really need help on this and could use some guidance please! Imagine you are in a game show. There are 10 prizes hidden on a game board with 100 spaces. One prize is worth $

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Question 1049351: I really need help on this and could use some guidance please!
Imagine you are in a game show. There are 10 prizes hidden on a game board with 100 spaces. One prize is worth $50, three are worth $20, and another six are worth $10. You have to pay $5 to the host if your choice is not correct. Let the random variable x be the winning.
(a)Complete the following probability distribution. (Show the probability in fraction format and explain your work)
x P(x)
-$5
$10
$20
$50
(b)What is your expected winning or loss in this game? Be specific in your answer whether it’s winning or loss. (Show work and round the answer to two decimal places)



(c) What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)
Any help is greatly appreciated!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
there are 100 spaces.

your probability of hitting any of the spaces is the same at 1/100.

1 out of 100 will get you 50.
3 out of 100 will get you 20.
6 out of 100 will get you 10.
the rest will get you nothing.

you put up 5 dollars so you're out 5 dollars to start with.

p(x) = -5 + 1/100 * 50 + 3/100 * 20 + 6/100 * 10

do the math and you get p(x) = -3.3

each ticket is expected to lose 3 dollars and 30 cents on the average.

you can do it another way.

the 50 dollar ticket will net you 45 dollars (50 - 5).
the 20 dollar tickets will net you 15 dollars (20 - 5).
the 10 dollar ticket will net you 5 dollars (10 - 5).
the rest of the tickets will net you -5 dollars (0 - 5).

p(x) = 1/100 * 45 + 3/100 * 15 + 6/100 * 5 + 90/100 * -5.

do the math and you get p(x) = -3.3

to find the standard deviation, you need to use the second form.

that form was:

p(x) = 1/100 * 45 + 3/100 * 15 + 6/100 * 5 + 90/100 * -5.

your distribution is as follows:

1 ticket nets you 45 dollars (50 - 5)
3 tickets net you 15 dollars (20 - 5)
6 tickets net you 5 dollars (10 - 5)
90 tickets net you -5 dollars (0 - 5).

you need to calculate the mean of this distribution and then you need to calculate the sum of squares of this distribution and then you can find the variance and the standard deviation.

there are calculators to do that for you, like the ti-84 plus, but i'll do it manually so i can show you how it's done.

i'll use excel so i can show you the method and how it evolves.

here's a picture of the excel worksheet.

$$$

i checked with an online calculator to make sure i did this right.
the online calculator confirms it to be correct.