Random Variable

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

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

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 standard deviation of the number of customers that make a purchase during the first hour that the store is open is

• 0.2
• 1.4
• 2.0
• 3.0

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

Which of the following random variables is NOT continuous?

• Amount of gasoline in a car.
• Time it takes to commute to work.
• Number of goals scored by a hockey team.
• Lifetime of a AAA battery.