QUESTION 138
A survey was conducted with 200 people about their preference for a type of music. The results are shown in the table below:

Type of music	Number of people
Rock	80
Pop	60
Samba	40
Other	20

The percentage of people who prefer Rock is
(A) $20\%$
(B) $30\%$
(C) $40\%$
(D) $50\%$
(E) $60\%$

QUESTION 140
The graph below shows the evolution of the price of a product over 5 months.
[Figure]
Based on the graph, the percentage increase in the price of the product from the first to the fifth month is
(A) $20\%$
(B) $25\%$
(C) $40\%$
(D) $50\%$
(E) $60\%$

The table presents part of the result of a spermogram (an exam that analyzes the physical conditions and composition of human semen).

\multicolumn{7}{|c|}{Spermogram}
Characteristics	Standard	30/11/2009	23/03/2010	09/08/2011	23/08/2011	06/03/2012
Volume (mL)	2.0 to 5.0	2.5	2.5	2.0	4.0	2.0
Liquefaction time (min)	Up to 60	35	50	60	59	70
pH	7.2 to 7.8	7.5	7.5	8.0	7.6	8.0
Sperm (unit / mL)	$> 20000000$	9400000	27000000	12800000	24200000	10200000
Leukocyte (unit / mL)	Up to 1000	2800	1000	1000	900	1400
Red blood cell (unit / mL)	Up to 1000	800	1200	200	800	800

To analyze the exam, one must compare the results obtained on different dates with the standard value of each evaluated characteristic. The patient obtained a result within the standards in the exam performed on
(A) $30/11/2009$.
(B) $23/03/2010$.
(C) $09/08/2011$.
(D) $23/08/2011$.
(E) $06/03/2012$.

A company recorded its performance in a given year through the graph, with monthly data of total sales and expenses.
Monthly profit is obtained by subtracting expenses from total sales, in that order.
Which three months of the year had the highest profits recorded?
(A) July, September, and December.
(B) July, September, and November.
(C) April, September, and November.
(D) January, September, and December.
(E) January, April, and June.

A bookstore sells books of the following literary genres: science fiction, self-help, romance, and biography. The graph presents the inventory of books that this bookstore has, by literary genre and by author's nationality, as well as the demand by literary genre, obtained through a survey conducted with its regular customers.
The bookstore manager will place an order for new copies only of the genre whose quantity in stock is insufficient to meet the demand identified by the survey.
The genre of book from which the manager should order more copies is
(A) science fiction, because it is the one with the highest demand.
(B) biography, because it is the genre with the lowest demand.
(C) self-help, because the quantity in stock is less than the demand.
(D) biography, because it is the genre with the smallest quantity of books in stock.
(E) romance, because it is the one with the smallest inventory of books by Brazilian authors.

In a school, all high school students practice one of three sports modalities offered as a physical activity, and each of them practices only one of these activities. The graphs provide some data related to the quantities of students who practice these sports modalities in this school, although some quantities have not been provided.
What is the number of high school students in this school?
(A) 720
(B) 360
(C) 320
(D) 288
(E) 240

The productivity of soybeans in a cultivated area is the average quantity of 50-kilogram sacks that are produced per hectare. The table presents the cultivated area and soybean productivity on a certain property, over five harvests, with periods of one year, from 2011 to 2016.

Harvest	$\mathbf{11\text{-}12}$	$\mathbf{12\text{-}13}$	$\mathbf{13\text{-}14}$	$\mathbf{14\text{-}15}$	$\mathbf{15\text{-}16}$
Cultivated area (hectare)	200	220	250	250	200
Productivity (sacks of $50\,\mathrm{kg}$ per hectare)	40	30	45	45	50

The line graph that represents the soybean production of this property, in tons, in these five harvests is
(A), (B), (C), (D), or (E) as indicated in the figures.

2. A middle school has 110 teachers in the junior high division and 150 teachers in the senior high division. Their gender ratios are shown in the figure. The number of female teachers in the school is
A. 167
B. 137
C. 123
D. 93 [Figure]

3. Based on the bar chart of China's annual carbon dioxide emissions (in units of 10,000 tons) from 2004 to 2013 shown below, which of the following conclusions is incorrect? [Figure]
A. Year-on-year comparison shows that 2008 had the most significant effect in reducing carbon dioxide emissions
B. China's efforts to control carbon dioxide emissions showed results in 2007
C. Since 2006, China's annual carbon dioxide emissions have shown a decreasing trend
D. Since 2006, China's annual carbon dioxide emissions are positively correlated with the year

Based on the bar chart of China's sulfur dioxide emissions (in units of 10,000 tons) from 2004 to 2013 shown below, which of the following conclusions is incorrect?
(A) Year-on-year comparison shows that 2008 had the most significant reduction in sulfur dioxide emissions
(B) China's treatment of sulfur dioxide emissions became evident in 2007
(C) Since 2006, China's annual sulfur dioxide emissions have shown a decreasing trend
(D) Since 2006, China's annual sulfur dioxide emissions are positively correlated with the year

12. In a marathon competition, the stem-and-leaf plot of the times (in minutes) of 35 athletes is shown in Figure 4 [Figure]
If the athletes are numbered 1-35 according to their times from best to worst, and 7 people are selected using systematic sampling, then the number of athletes with times in the interval $[139, 151]$ is $\_\_\_\_$.

14. An e-commerce company conducted a statistical survey of 10,000 online shoppers' consumption in 2014. The consumption amount (in units of 10,000 yuan) falls within the interval [0.3, 0.9]. The frequency distribution histogram is shown in the figure below.
(1) In the histogram, $\mathrm { a } =$ $\_\_\_\_$.
(2) Among these shoppers, the number of shoppers with consumption amount in the interval [0.5, 0.9] is $\_\_\_\_$. [Figure]

17. An enterprise wants to understand the service quality of a certain department to its employees. It randomly surveyed 50 employees. Based on the evaluation scores of these 50 employees for the department, a frequency distribution histogram was drawn (as shown in the figure). The sample data are grouped into intervals [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100].
(1) Find the value of $a$ in the frequency distribution histogram;
(2) Estimate the probability that an employee's evaluation score is not less than 80;
(3) From the surveyed employees whose scores are in $[ 40,60 ]$, randomly select 2 people. Find the probability that both of their scores are in $[ 40,50 ]$. [Figure]

18. (This question is worth 12 points). A company randomly surveyed 40 users from regions $A$ and $B$ respectively to understand user satisfaction with its products. Based on user satisfaction scores, a frequency distribution histogram of user satisfaction scores in region $A$ and a frequency distribution table of user satisfaction scores in region $B$ were obtained.
Frequency Distribution Histogram of User Satisfaction Scores in Region A [Figure]

Satisfaction Score Interval	\multicolumn{5}{|c|}{Frequency Distribution Table of User Satisfaction Scores in Region B}
Frequency	$[ 50,60 )$	$[ 60,70 )$	$[ 70,80 )$	$[ 80,90 )$	$[ 90,100 ]$
	2	8	14	10	6

(I) Draw the frequency distribution histogram of user satisfaction scores in region $B$ on the answer sheet, and compare the mean and dispersion of satisfaction scores in the two regions through this histogram (no need to calculate specific values, just provide conclusions); [Figure] (II) Based on user satisfaction scores, user satisfaction levels are divided into three categories:

Satisfaction Score	Below 70	70 to 89	At least 90
Satisfaction Level	Dissatisfied	Satisfied	Very Satisfied

Estimate which region has a higher probability that a user's satisfaction level is dissatisfied, and explain the reasoning.

A company conducted a survey of 20 users from regions A and B respectively to understand user satisfaction with its products. The satisfaction scores are as follows:
Region A: 62, 73, 81, 92, 95, 85, 74, 64, 53, 76, 78, 86, 95, 66, 97, 78, 88, 82, 76, 89
Region B: 73, 83, 62, 51, 91, 46, 53, 73, 64, 82, 93, 48, 65, 81, 74, 56, 54, 76, 65, 79
(I) Complete the stem-and-leaf plot for user satisfaction scores in both regions based on the two sets of data, and compare the mean and dispersion of satisfaction scores between the two regions through the stem-and-leaf plot (no need to calculate exact values, just draw conclusions);
(II) Based on user satisfaction scores, classify user satisfaction into three levels from low to high:
Satisfaction Score: Below 70, 70 to 89, At least 90 Satisfaction Level: Dissatisfied, Satisfied, Very Satisfied
Let event $C$: ``The satisfaction level of users in region A is higher than that of users in region B''. Assume the evaluation results from the two regions are independent. Based on the given data, using the frequency of event occurrence as the probability of the corresponding event, find the probability of event $C$.

To improve production efficiency, a factory conducted technological innovation activities and proposed two new production methods for completing a production task. To compare the efficiency of the two methods, 40 workers were selected and randomly divided into two groups of 20 each. The first group used the first production method, and the second group used the second production method. Based on the time (in minutes) taken by workers to complete the production task, a stem-and-leaf plot was drawn.
(1) Based on the stem-and-leaf plot, which production method has higher efficiency? Explain your reasoning.
(2) Find the median $m$ of the time taken by all 40 workers to complete the production task, and fill in the contingency table with the number of workers whose completion time exceeds $m$ and does not exceed $m$ for each production method.

17. (12 points) To understand the retention levels of two types of ions in mice, the following experiment was conducted: 200 mice were randomly divided into groups $A$ and $B$, with 100 mice in each group. Group $A$ mice were given a solution of ion type 1, and group $B$ mice were given a solution of ion type 2. Each mouse was given the same volume of solution with the same molar concentration. After a period of time, the percentage of ions retained in the mice's bodies was measured using a scientific method. Based on the experimental data, the following histograms were obtained: [Figure] [Figure]
Let $C$ be the event: ``the retention percentage of ion type 2 in the body is at least 5.5.'' Based on the histogram, the estimated value of $P ( C )$ is 0.70.
(1) Find the values of $a$ and $b$ in the histogram for ion type 2's retention percentage.
(2) Estimate the mean retention percentages for ions of type 1 and type 2 respectively (use the midpoint of each interval as the representative value for data in that interval).

17. (12 points) To understand the residual levels of two types of ions in mice, the following experiment was conducted: 200 mice were randomly divided into groups A and B, with 100 mice in each group. Group A mice were given a solution of ion type 甲, and group B mice were given a solution of ion type 乙. Each mouse was given the same volume of solution with the same molar concentration. After a period of time, a scientific method was used to measure the percentage of ions remaining in the mice's bodies. Based on the experimental data, the following histograms were obtained: [Figure]
Let $C$ be the event: ``the residual percentage of ion 乙 in the body is not less than 5.5''. Based on the histogram, the estimated value of $P ( C )$ is 0.70.
(1) Find the values of $a$ and $b$ in the histogram for the residual percentage of ion 乙;
(2) Estimate the mean residual percentage for ions 甲 and 乙 respectively (use the midpoint of each interval as the representative value for data in that interval).

2. To understand the rural economic situation in a certain area, a sample survey was conducted on the annual household income of farmers in that area. The survey data on farmers' annual household income was organized into the following frequency distribution histogram: [Figure]
Based on this frequency distribution histogram, which of the following conclusions is incorrect?
A. The estimated proportion of farmers with annual household income below 4.5 ten thousand yuan is $6 \%$
B. The estimated proportion of farmers with annual household income not less than 10.5 ten thousand yuan is $10 \%$
C. The estimated average annual household income of farmers in this area does not exceed 6.5 ten thousand yuan
D. It is estimated that more than half of the farmers in this area have annual household income between 4.5 and 8.5 ten thousand yuan

2. To understand the rural economic situation in a certain area, a sampling survey was conducted on the annual household income of farmers. The survey data on farmers' annual household income was organized into the following frequency distribution histogram. Based on this frequency distribution histogram, which of the following conclusions is incorrect?
A. The estimated proportion of farmers with annual household income below 4.5 ten thousand yuan is 60\%
B. The estimated proportion of farmers with annual household income not less than 10.5 ten thousand yuan is 10\% [Figure]
C. The estimated average annual household income of farmers in this area does not exceed 6.5 ten thousand yuan
D. It is estimated that more than half of the farmers have annual household income between 4.5 and 8.5 ten thousand yuan

In a data set where not all values repeat equally, each value that repeats most frequently is called the mode of this data set.
All 48 students in a class took a mathematics exam, and the numerical distribution of the scores these students received from this exam is given in the column graph below.
The modes of the data set formed by the scores from this exam were found, and the total number of students with scores equal to these values was 32. Additionally, the number of students in this class who scored above 70 on this exam was calculated as 38.
Accordingly, how many students in this class scored 65 on this exam?
A) 2
B) 3
C) 4
D) 5
E) 6