MA202 Unit 4 Review

Data Sets

100

Consider the data set

{5, 1, 8, 9, 3, 1, 2, 17, 1, 13}.

Find the mean, median, and mode of the data set.

The mean is 6, the median is 4, and the mode is 1.

200

Compute the IQR of the data set

{5, 2, 8, 1, 9, 9, 2, 4, 3}

6.5

300

4 People take an exam. Their average score is 78. After a fifth student takes the exam, the new average is 80. What was the fifth student's score?

88

Probability

100

If there are 23 distinct marbles in a bag, and I pull one marble out, replace it, then pull another, what is the probability that I pull the same marble twice?

1/23.

200

There are 5 green candies, 3 blue candies, and 7 red candies in a bag. If you pull one piece of candy out of the bag, eat it, then pull another piece of candy out of the bag, what is the probability that both candies were blue?

1/35

300

Seven people are in a room. Every pair of people shakes hands. Three people in the room are painters who were just working on painting a wall blue, so their hands have blue paint on them. If two people have blue paint on their hands, we will call a hand shake between them a blue shake. What is the probability that a handshake that occurred between two people in the room is a blue shake?

1/7.

Expected Value

100

If an experiment has numerical outcomes

a_1,a_2,...,a_n

with respective probabilities

P_1,P_2,...,P_n,

what is the expected value of the experiement?

E = a_1P_1 + a_2P_2 + ... + a_nP_n.

200

If an experiment has two numerical outcomes, a₁ and a₂, with the property that a₁ = -a₂, each equally probable, what is the expected value of this experiment?

0

300

Suppose there is a game that costs $5 to play, wherein a player pulls a marble from a bag containing 10 green marbles, 8 blue marbles, and 2 red marbles. If the player draws a green marble, they are given $0. If they draw a blue marble, they are given $4. If they draw a red marble, they are given $10. Should you play this game?

No!

(Expected Value = -$2.40)