Random Variables

Which of the following random variables should be considered continuous?

• The number of brothers a randomly chosen person has
• The number of orders received by a mail order company in a randomly chosen week
• The number of cars owned by a randomly chosen adult male
• The time it takes a randomly chosen woman to run 100 meters

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?

• $2.50

• $1

• $2.50

• $4

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 standard deviation of X?

• $1
• $1.35
• $1.41
• $1.78

What is the difference between a discrete random variable and a continuous random variable?

• A discrete random variable takes all values in an interval of numbers while a continuous random variable has a fixed set of possible values with gaps between.
• A discrete random variable has a fixed set of possible values with gaps between while a continuous random variable takes all values in an interval of numbers.
• A discrete random variable takes only negative numbers while a continuous random variable takes both positive and negative numbers.
• A discrete random variable takes both positive and negative numbers while a continuous random takes only negative numbers.

A regular deck of cards has 4 aces. You are asked to pick one card from the deck. If the card you picked is an ace you win $5! However if you pick any other card, you lose $2. If you play this game many times, on average how much would you expect to win? Just a reminder....a deck contains 52 cards. :-)

• About $1.46

• About $4.46

• About -$1.46

• About $3

Multiplying/Dividing each value of a random variable by a number x will...

I. Multiply/Divide the mean, median, quartiles, and percentiles by number x

II. Change the shape of the distribution.

III. Multiply/Divide the range, IQR, standard deviation by |x|

• I and II

• I and III

• II and III

• I, II, and III

What doe this formula calculate: x₁p₁+x₂p₂+x₃p₃+...=Σx_ip_i

• Standard deviation

• Mean

• Expected Value

• Both mean and expected value

The same potato chip company reports that their bags of family sized chips each follows an approx. Normal distribution with a mean of 10.72 ounces and a standard deviation of 0.2 ounces. If the company wants to pack these chips into boxes that contain 6 bags, what would be the mean and standard deviation of the total weight of a box containing 6 bags of chips? The empty boxes have a mean weight of 10 ounces and a standard deviation of 0.05 ounces

• Mean = 74.32 oz and St.Dev = .4924

• Mean = 74.32 oz and St.Dev = .2425

• Mean = 75.04 oz and St.Dev = .4924

• Mean = 75.04 oz and St.Dev = .2425

At a warehouse sale 100 customers are invited to choose one of 100 identical boxes. Five boxes contain $300 HD TVs, 25 boxes contain $150 camcorders, and the remaining boxes contain $75 digital cameras. What should a customer be willing to pay to participate in the sale?

• $155
• $98
• $240
• $105

An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is .2, and of having a major accident, .05, how much can the insurance company expect to make on a policy?

• $250

• $300

• $150

• $450