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Instructor(s): Janine Tiefenbruck
This exam was administered in-person. Students were allowed one page of double-sided handwritten notes. No calculators were allowed. Students had 3 hours to take this exam.
The Hunger Games is a young adult dystopian fictional novel. The events take place in the future in the fictional country of Panem, which consists of 12 impoverished districts and a wealthy metropolitan area called the Capitol.
The plot centers around an annual televised competition called the Hunger Games, in which children from the districts are forced to compete in a battle to the death. The participants, called tributes, are randomly selected via a lottery system.
The competition takes place in an arena that is specially designed for this purpose, and usually lasts several days or weeks, until only one tribute survives. The entire event is turned into a spectacle, which is broadcast throughout Panem as a way for the oppressive government to remind district residents of their powerlessness.
The main character and protagonist of The Hunger Games is Katniss Everdeen, a 16-year old girl from District 12 who competes in the 74th annual Hunger Games. After a life of poverty and near starvation, her experience in the Hunger Games arena further fuels her hatred of the government and lights a fire in her to fight back against the oppression.
Notes:
import babypandas as bpd, import numpy as np,
and import scipy.In an annual ceremony known as the reaping, tributes are selected to represent their district in the Hunger Games. One male and one female tribute from each district are randomly selected via a lottery drawing.
Every child between the ages of 12 and 18 (inclusive) has tickets entered into the drawing for their sex and district (e.g. girls from District 12). The number of tickets entered is dependent on age.
Starting at age 12, each child receives one ticket in the lottery. For each year after that, they receive one additional ticket, added to the total from the previous year. For example, 13-year-olds have two tickets, 14-year-olds have three tickets, and so on.
In this problem, we will consider only tickets corresponding to girls from District 12, and look at the distribution of these tickets according to the age of the person they represent. A density histogram for these tickets is shown below.
Which of the following statements about this distribution is correct?
The mean is less than the median.
The mean is the same as the median.
The mean is greater than the median.
It is impossible to determine the relationship between the mean and
The histogram from the previous page is repeated below for your reference.
Suppose the rules of the Hunger Games were changed to eliminate 18-year-olds. If we plotted a new density
histogram of the distribution of ages for tickets corresponding to girls
from District 12 aged 12 to 17,
how would the height of the [13, 14) bar change?
Let h be the height of this bar in the original histogram. Give its height in the new histogram in terms of h.
What is the most common age among girls from District 12 aged 12 to 18? Remember, the distribution above is for all tickets, and older girls have more tickets.
12 ( ) 13 ( ) 14 ( ) 15 ( ) 16 ( ) 17 ( ) 18