Chapter 6: Random Variables

Which of the following is not a random variable?

• The heights of randomly-selected buildings in New York City.

• The suit of a card randomly-selected from a 52-card deck.

• The number of children in randomly-selected households in the United States.

• The amount of money won (or lost) by the next person to walk out of a casino in Las Vegas.

A random variable is

• a hypothetical list of the possible outcomes of a random phenomenon.
• any phenomenon in which outcomes are equally likely.
• any number that changes in a predictable way in the long run.
• a variable whose value is a numerical outcome associated with a random phenomenon.

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 that you win. 
Which of the following is the expected value of X?

• $1.00
• $2.50
• $4.00
• $6.00

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

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.
The mean number of customers that make a purchase during the first hour that the store is open is:
   

• 2.0
• 2.5
• 2.9
• 3

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

The weight of written reports produced in a certain department has a Normal distribution with mean 60 g and standard deviation 12 g. The probability that the next report will weigh less than 45 g is

• .1056
• .3944
• .1042
• .8944

Your friend Albert has invented a game involving two ten-sided dice.  One of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens.  He won’t tell you how many of each number there are on the faces, but he does tell you that if X = the result of a single roll of the first die and Y = the result of a single roll of the second die, then μ_x=3.6, σ_x=0.8, μ_y=8.0 and σ_y=0.9. Let Z = the sum of the two dice when each is rolled once.
What is the expected value of Z?

• 1.7
• 4.4
• 5.8
• 11.6

Mike's job is just a few bus stops away from his house.  While it can be faster to take the bus to work, it’s more variable, because of variations in traffic.  He estimates that the commute time to work by bus is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 4 minutes.  The commute time if he walks to work is also approximately Normally distributed with a mean of 16 minutes with a standard deviation of 1 minute.  What is the probability that the bus will be faster than walking?

• .8340
• .8485
• .8980
• .9756

In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes are independent, which of the following represents the probability that you win at least once?

• (0.2)⁵
• 1-(0.2)⁵
• 1-(0.8)⁵
• (₅C₂)(0.2)(0.8)⁴

A college basketball player makes 5/6 of his free throws. Assuming free throw attempts are independent, the probability that he makes exactly three of his next four free throws is

• 4(1/6)³(5/6)¹
• (1/6)³(5/6)¹
• (1/6)¹(5/6)³
• 4(1/6)¹(5/6)³

A poll shows that 60% of the adults in a large town are registered Democrats.  A newspaper reporter wants to interview a local democrat regarding a recent decision by the City Council.
If the reporter asks adults on the street at random, what is the probability that he will find a Democrat by the time he has stopped three people?

• .936
• .216
• .144
• .096