few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Your response, in json format:
{
  "explanation": "This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.",
  "answer": "C"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000674

5
options: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
problem_activity: Task
A famous arcade in a seaside resort town consists of many different games of skill and chance.  In order to play a popular “spinning wheel” game at Fred's Fun Factory Arcade, a player is required to pay a small, fixed amount of 25 cents each time he/she wants to make the wheel spin. When the wheel stops, the player is awarded tickets based on where the wheel stops -- and these tickets are then redeemable for prizes at a redemption center within the arcade.
Note: this particular game has no skill component; each spin of the wheel is a random event, and the result from each spin of the wheel is independent of the results of previous spins.
The wheel awards tickets with the following probabilities:
|  1 ticket   | 35% |
|-------------|-----|
|  2 tickets  | 20% |
|  3 tickets  | 20% |
|  5 tickets  | 10% |
| 10 tickets  | 10% |
| 25 tickets  | 4%  |
| 100 tickets | 1%  |
(Note: A picture of a wheel fitting these parameters is included.)
If a player were to play this game many, many times, what is the expected (average) number of tickets that the player would win from each spin?
The arcade often provides quarters to its customers in $5.00 rolls. Every day over the summer, a young boy obtains one of these quarter rolls and uses all of the quarters for the spinning wheel game. In the long run, what is the average number of tickets that this boy can expect to win each day using this strategy?
One of the redemption center prizes that the young boy is playing for is a trendy item that costs 300 tickets.  It is also available at a store down the street for $4.99. Without factoring in any enjoyment gained from playing the game or from visiting the arcade, from a strictly monetary point of view, would you advise the boy to try and obtain this item based on arcade ticket winnings or to just go and buy the item at the store?  Explain.
The histogram below summarizes the results of 90 summer days of the boy playing the game using his "$5 roll per day" strategy. The first bar in the histogram represents those days where 40 to 59 tickets were won.
[IMG]
For approximately what percentage of the 90 days did the boy earn fewer than 100 tickets in a day?
For approximately what percentage of the 90 days did the boy earn 200 or more tickets in a day?
For approximately what percentage of the 90 days did the boy earn 300 or more tickets in a day?
To maintain the spinning wheel game machine, the arcade manager adopts a strategy of emptying the money box (that's where the quarters go after they are inserted in the machine) each time she refills the machine with a new roll of tickets. The ticket refill rolls contain 5000 tickets, and the machine is designed to hold $1300 in quarters in its money box. Assume that the machine was fully loaded with 5000 tickets and had an empty money box when it was first used. Using the manager's maintenance strategy, is there any chance that the money box could become completely full with quarters or overflow with quarters? Explain.
Arcade Wheel
| Color  | Tickets |
|--------|---------|
| Orange |    1    |
| Green  |    2    |
|  Blue  |    3    |
| Yellow |    5    |
| Purple |   10    |
| Black  |   25    |
|  Red   |   100   |
Graphics Note: The wheel diagram was developed in Microsoft Excel using its "Pie Chart" graph building feature.  The intent is that each wedge represents 1% of the pie (3.6 degrees).  There are 35 orange wedges (each representing a win of 1 ticket) to correspond to the 35% probability of obtaining 1 ticket in a spin, 20 green wedges (each representing a win of 2 tickets) to correspond to the 20% probability of obtaining 2 tickets in a spin, and so on.
[IMG]


correct_option_index: 1