AP Stat Ch. 6 Quiz

In the Florida scratch-card lottery, the numbers and values of prizes awarded for every 100,000 cards sold are Number of cards = 10, Payoff = $1,000 ... Number of cards = 1000, Payoff = $50 Number of cards = 5000, Payoff = $5 The expected payoff per card sold is

$0.85

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. X = 0, P(X) = 0.1 ... X = 1, P(X) = 0.1 ... X = 2, P(X) = 0.1 ... X = 3, P(X) = 0.1 ... X = 4, P(X) = 0.6 Consider the following game. You pay me an entry fee of x dollars; then I roll a fair die. If the die shows a number less than 3 I pay you nothing; if the die shows a 3 or a 4, I give you back your entry fee of x dollars; if the die shows a 5, I will pay you $1; and if the die shows a 6, I pay you $3. What value of x makes the game fair (in terms of expected value) for both of us?

$1

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

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 standard deviation of X?

$1.41

The probability distribution of a continuous random variable X is given by the density curve below *shaded box-shaped graph with 0, 1, 2 on x-axis and nothing on y-axis* The probability that X = 1.5 is

0

In the Florida scratch-card lottery, the numbers and values of prizes awarded for every 100,000 cards sold are Number of cards = 10, Payoff = $1,000 ... Number of cards = 1000, Payoff = $50 Number of cards = 5000, Payoff = $5 The probability that a random scratch-card will pay off is

0.0601

In a population of students, the number of calculators a student owns is a random variable X described by the following probability distribution X = 0, P(X) = 0.2 ... X = 1, P(X) = 0.6 ... X = 2, P(X) = 0.2 Which of the following is the standard deviation of X?

0.6325

Z | 0 | 1 | 2 | 3 | 4 P(Z) | 0.0625 | 0.2500 | 0.3750 | 0.2500 | 0.0625 The probability of at least one tail given that Z = the number of heads in four flips

0.9375

In a population of students, the number of calculators a student owns is a random variable X described by the following probability distribution X = 0, P(X) = 0.2 ... X = 1, P(X) = 0.6 ... X = 2, P(X) = 0.2 Which of the following is the mean of X?

1

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. X = 0, P(X) = 0.1 ... X = 1, P(X) = 0.1 ... X = 2, P(X) = 0.1 ... X = 3, P(X) = 0.1 ... X = 4, P(X) = 0.6 The standard deviation of the number of customers that make a purchase during the first hour that the store is open is

1.4

Let X be the outcome of rolling a fair six-sided die. P(2 <_ X < 5) =

1/2

The probability distribution of a continuous random variable X is given by the density curve below *shaded box-shaped graph with 0, 1, 2 on x-axis and nothing on y-axis* The probability that X is between 0.5 and 1.5 is

1/2

The probability distribution of a continuous random variable X is given by the density curve below *shaded box-shaped graph with 0, 1, 2 on x-axis and nothing on y-axis* The probability that X is at least 1.5 is

1/4

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. X = 0, P(X) = 0.1 ... X = 1, P(X) = 0.1 ... X = 2, P(X) = 0.1 ... X = 3, P(X) = 0.1 ... X = 4, P(X) = 0.6 The mean number of customers that make a purchase during the first hour that the store is open is

3.0

I roll a pair of fair dice and let X = the sum of the spots on the two sides facing up. The probability the X is 2, 11, or 12 is

4/36

A variable whose value is a numerical outcome of a random phenomenon is called

A random variable

A random variable is

A variable whose value is a numerical outcome associated with a random phenomenon

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. X = 0, P(X) = 0.1 ... X = 1, P(X) = 0.1 ... X = 2, P(X) = 0.1 ... X = 3, P(X) = 0.1 ... X = 4, P(X) = 0.6 The density curve for a continuous random variable X has which of the following properties?

All of the above a. the prob of any event is the area under the density curve between the values of X that make up the event b. the total area under the density curve for X must be exactly 1 c. P(X=a) = 0 for any constant a. d. The density curve lies completely on or above the horizontal axis. e. ALL OF THE ABOVE

Suppose there are three balls in a box. on one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1,2), (1,3), (2,3)}. Let X be the sum of the numbers on two balls selected. Which of the following is the correct probability distribution for X?

No.|Prob. ----|------- 3 | 1/3 ----|------- 4 | 1/3 ----|------- 5 | 1/3

Flip a coin four times. If Z = the number of heads in four flips, then the probability distribution of Z is given in the table below: Z | 0 | 1 | 2 | 3 | 4 P(Z) | 0.0625 | 0.2500 | 0.3750 | 0.2500 | 0.0625

P(Z <_ 3)

Which of the following is not a random variable

The response of randomly-selected people to the question, "Did you eat breakfast this morning?"

Which of the following is not a random variable

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

Which of the following random variables should be considered continuous

The time it takes for a randomly chosen woman to run 100 meters

An ecologist studying starfish populations collects the following data on randomly selected 1-meter by 1-meter plots on a rocky coastline --The number of starfish in the plot --The total weight of starfish in the plot --The percentage of area in the plot that is covered by barnacles (food for starfish) --Whether or not the plot is underwater midway between high and low tide How many of these measurements can be treated as contituous random variables and how many as discrete random variables?

Two continuous, one discrete, and a fourth that cannot be treated as random variable

Which of the following is true about every random variable i. It takes on numerical or categorical values ii. It describes the results of a random phenomenon iii. Its behavior can be described by a probability distribution

ii and iii