Expected Value and Standard Deviation

Choose an American household at random. What is the expected number of cars for that household?

• 1.75

• 1.84

• 2.00

• 2.50

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household? HINT: A Probability table may be helpful.

• 2.00

• 2.13

• 1.97

• 1.27

A fair, 6-sided dice is thrown 120 times.

Roughly how many times would you expect the number 5 to come up?

• 6

• 10

• 12

• 20

The table shows the probability distribution of a fair six-sided die. Determine 𝐸(𝑋).

give your answer to 1 decimal place.

(a)  

You roll a standard die. You win $12 if you roll a six, $6 if you roll a one, and $0 if you roll anything else. What is the expected value of a single roll?

• $3

• $18

• $9

• $2

You are playing a game by drawing a card from a standard deck and replacing it. If the card is a face card, you win $30. If it is not a face card, you pay $2. There are 12 face cards in a deck of 52 cards. What is the expected value of playing the game?

Write your answer to 2 decimal places. leave out the $

(a)  

The function in the given table is a probability function of a discrete random variable 𝑋. Given that the expected value of 𝑋 is 6.5, find the value of A.

(a)  

13 students took an exam; 8 students got 6 marks, 3 students got 10 marks, and 2 students got 2 marks. Given that 𝑋 denotes the number of marks received, find the expected value of x. Write your answer to 2 decimal places.

(a)  

13 students took an exam; 8 students got 6 marks, 3 students got 10 marks, and 2 students got 2 marks. Given that 𝑋 denotes the number of marks received, find the standard deviation of x. Write your answer to 2 decimal places.

(a)  

Your friend shuffles a standard deck of cards and says to pick one. If you pick a face card (Jack, Queen, King of each suit) your friend will give you $10. If you pick anything else, you owe your friend $5. How much should you expect to win or lose by playing this game?

(Write the figure only to 2 decimal places, leave out the $)

(a)