AMC
Estimation
Statistics
Coding/Math modeling
Fun
100
How many distinguishable arrangements are there of 1 brown tile, 1 purple tile, 2 green tiles, and 3 yellow tiles in a row from left to right? (Tiles of the same color are indistinguishable.)
420
100
For a large data set, the mean and median are often close in value. If the mean of a data set is 98 and the data is normally distributed, the median is approximately equal to which value?
98
100
In a data set, if the mean is 30 and the variance is 16, what is the standard deviation?
4
100
In Python, which library is commonly used for numerical operations and working with arrays, often used in data science and mathematical modeling?
NumPy
100
What is the name of the famous sequence where each number is the sum of the two preceding ones, starting from 0 and 1, and how is it used in nature?
The Fibonacci Sequence
200
Ms. Carr asks her students to read any 5 of the 10 books on a reading list. Harold randomly selects 5 books from this list, and Betty does the same. What is the probability that there are exactly 2 books that they both select?
25/63
200
Estimate the number of digits in 5^20
14
200
This term describes a relationship where the value of one variable increases as the value of another variable decreases. What is this type of relationship called?
Negative Correlation
200
What is the concept of “Big-O” notation in computer science, and how is it used to evaluate the efficiency of an algorithm?
It provides a high-level understanding of the algorithm's efficiency.
200
You have $10 and are playing a fair game where you can either win or lose $1 each time you play. What is the probability that you will eventually lose all your money if you keep playing?
The probability of losing all your money is 100% if you keep playing indefinitely, assuming that the game is fair and you can continue playing until you lose.
300
How many positive even multiples of 3 less than 2020 are perfect squares?
7
300
Estimating the value of log10500 using the properties of logarithms, what is the approximate value?
2.7
300
In a simple linear regression analysis, if the equation is Y=2+0.5X and the correlation coefficient r is 0.8, what is the coefficient of determination R^2?
0.64
300
In regression analysis, this measure assesses the goodness of fit of a model by comparing the variance of the residuals to the variance of the observed data.
What is the R-squared value?
300
The Monty Hall Problem: In a game show scenario, you choose one of three doors. Behind one door is a car, and behind the other two are goats. After the host opens one of the doors revealing a goat, should you switch doors to maximize your chances of winning the car?
The probability of winning the car increases to 2/3 if you switch, compared to 1/3 if you stick with your original choice.
400
The decimal representation of
consists of a string of zeros after the decimal point, followed by a 
and then several more digits. How many zeros are in that initial string of zeros after the decimal point?
26
400
Given the data set {2, 4, 6, 8, 10}, estimate the standard deviation.
2.83
400
In a box of 12 light bulbs, 3 are defective. If 4 bulbs are randomly selected, what is the probability that exactly 1 of the 4 selected bulbs is defective?
54/91
400
This technique is used to determine the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.
Linear Regression
400
In a building with 100 floors, an elevator starts on the ground floor and randomly chooses a floor to go to. What is the expected number of floors the elevator will visit before returning to the ground floor?
The expected number of floors visited is 50. This is because each floor has an equal probability of being visited.
500
There are 10 people standing equally spaced around a circle. Each person knows exactly 3 of the other 9 people: the 2 people standing next to her or him, as well as the person directly across the circle. How many ways are there for the 10 people to split up into 5 pairs so that the members of each pair know each other?
13
500
If you invest $1,000 at an annual interest rate of 6%, compounded yearly, estimate the amount of money after 5 years.
$1,338
500
In a class of 25 students, what is the probability that at least two students share the same birthday? Assume there are 365 days in a year and ignore leap years.
0.5687 or 56.87%
500
What is the name of the mathematical field that focuses on finding the best solution from a set of feasible solutions, often subject to constraints, and includes techniques such as linear programming and integer programming?
Optimization
500
What is the term for a phenomenon in dynamical systems where small changes in initial conditions lead to vastly different outcomes, making long-term prediction practically impossible?
The butterfly effect