TEST ON RANDOM VARIABLES

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4 and if the number of spots showing is 1, 2 or 3, you win nothing. Let X be the amount you win.  What is the expected value of X?

• $
• $1
• $2.50
• $4

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. What is the average number of customers that the owner can expect to make a purchase in the first hour of opening?

• 0.2

• 1.4

• 2.0

• 3.0

Cool TV game show
Players win prizes with probabilities shown:
P($0) = .70
P($500) = .25
P($5,000) = .05
What are the mean and the standard deviation of the prize variable?

• Mu = $375; sigma = $361
• Mu = $375; sigma = $1,083
• Mu = $1,833; sigma = $1,816
• Inadequate info is provided.

You pick a card from a deck.  If you get a face card, you win $5.  If you get an ace, you win $30 plus an extra $60 for the ace of hearts.  For any other card you win nothing. Find the expected value you will win.

• $5.00
• $3.85
• $4.04
• $4.62

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

• 1.75
• 1.84
• 2.00
• 2.50

Is the distribution below a probability distribution? Why or why not?

• Yes. All P(x) values are between 0 and 1, and ∑P(x) = 1
• No, not all P(x) values are between 0 and 1.
• No, ∑P(x) ≠ 1.

Tags

CCSS.HSS.MD.A.1

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

The table represents the probability of guessing correct on a 5 question true-false quiz.  Find the probability for at least 4 questions correct.

• .03125
• .15625
• .3125
• .1875

Tags

CCSS.HSF-LE.A.1C

On an eight question multiple choice quiz with 4 answers for each question, what is the probability of guessing and getting 6 correct answers?

• .004
• .109
• .003
• .9996

Tags

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

P(Sandals):

• 16/22
• 20/36
• 5/9
• 20/16

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.A.4

Is this a probability distribution?

• No
• Yes