Expected Values – Probabilities and Statistics

#1) Find the expected value for the probability model shown below.

Value $2 $4 $8 $30Probability 0.25 0.5 0.17 0.08

#2) Find the missing value (???) in the probability model shown below.

Value $2 $5 $8 $11Probability 0.18 0.33 ??? 0.28

#3) In the probability model given below, the expected value is – $1.55. Find the missing value, x.

Value $4 -$5 x -$8

Probability 0.20 0.45 0.15 0.20

#4) A large number of people were polled and asked which of four different animals were their favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you decide to carry out a simulation given these percentages. You decide to select two digits at a time. Which would be a proper assignment of digits for these teams?

a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtleb) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtlec) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtled) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtlee) None of These

#5) The expected value for the following scenario is $1.60. Write two different equations that give both a simplified equation using the expected value and a simplified equation for the total of all probabilities in the probability model.

Value $3 -$4 $17Probability x y 0.08

#6) Suppose that there are 513 students who are currently enrolled in AP Calculus and that we are looking for five randomly selected students to survey about their experiences in AP Calculus. The digit combinations 001-513 are assigned to represent the 513 students currently enrolled in AP Calculus. Using the random digits below, what are the numbers of the five students that will be selected for the survey? 71548 15233 53946 68713 72468 27601 13703 88692

Student 1 = #_____, Student 2 = #_____, Student 3 = #_____, Student 4 = #_____, Student 5 = #_____

#7) If you buy a ticket in a certain lottery game, 30% of the players will get paid $1, 20% of the players will get paid $6, and 5% of the players will get paid $55. All other players get paid nothing. What is the expected amount that a player of this lottery game will get paid?

#8) In a certain card game you draw one card off a standard deck of 52 cards. If you draw a spade you get paid $12, if you draw a red Ace you get paid $20, and if you draw a red Queen you get paid $38. If you draw anything else, you get paid nothing. What should this game cost if it is to be a fair game? Use fractions in your work and then calculate the answer as a decimal rounded to 4 decimal places.

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