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Talia wants to play a basketball game at a carnival. the game cost the player $5 to play, and the player gets to take too long distance shots. if they missed both shots, they get nothing. if they make one shot, they get their $5 back. Thalia has a 40% chance of making this type of shot.

here is the probability distribution of x= the amount of money Talia gains from playing the game.

x= money gain -$5 $0 $5
P(x) 0.36 0.48 0.16


Given that μx = -$1, calculate Θ x.
round your answer to two decimal places


Θx = _______ dollars

Respuesta :

veronikali2002

Answer:3.46$

Step-by-step explanation:

The answer is "3.464".

Probability distribution:

[tex]\to x \ \ \ \ \ \ \ -\$5 \ \ \ \ \ \ \ \$0 \ \ \ \ \ \ \ \$5\\\\\to P(x) \ \ \ \ \ \ \ 0.36 \ \ \ \ \ \ \ 0.48 \ \ \ \ \ \ \ 0.16\\\\[/tex]

[tex]\to \mu_{x}= Mean\ (X)= E(X) \ = - \$ 1\\\\\to \sigma^{2}_{x}= \Sigma_{x} x^2 p(x)- (\mu_{x})^2\\\\[/tex]  

         [tex]=(-5)^2 \times 0.36 + 0+ (5)^2 \times 0.16 - (-1)^2\\\\=25 \times 0.36 + 0+ 25 \times 0.16 - 1\\\\=9 + 0+ 4 - 1\\\\= 13-1\\\\=12\\\\[/tex]

Therefore,  

[tex]\to \sigma_{x}=\sqrt{12}= \$ 3.464[/tex]

Therefore, the final answer is "3.464".

Learn more about the probability distribution:

brainly.com/question/22631589