School Improvement in Maryland

Public Release Item: Public Release items have appeared on HSA forms and then are released for public viewing and use. Releasing items is one step to ensuring that schools, districts, and other stakeholders understand how the core learning goals are assessed on the HSA.

Goal 3 Data Analysis And Probability

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

Indicator 3.2.1 The student will make informed decisions and predictions based upon the results of simulations and data from research.

Selected Response Item - Released in 2001

A quality control engineer for the Have Fun Toys Company tested 800 video game cartridges and found 3 defective cartridges. The company plans to produce 500,000 video game cartridges this year. Based on the findings, how many video game cartridges can be expected to be defective?

  1. 16
  2. 20
  3. 1,875
  4. 2,000
/share/clg/xml/public_release/mathematics/2001_321_alg48.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2001

A movie producer is considering two different endings for a movie. To decide which ending is better, the producer randomly selected two groups of people to watch each ending. There were 200 people in each group. The two groups rated the movie endings on a scale of 1 to 100. The box-and-whisker plots below show a summary of their results.
Complete the following in the answer box:
  • Which ending had a higher median rating? Use mathematics to justify your answer.
     
  • Which ending had a wider range of ratings? Use mathematics to justify your answer.
     
  • Based on the data shown in the box-and-whisker plots, the movie producer decided that the first ending was better than the second ending. Is this a valid conclusion to make from the data given? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2001_321_alg49.xml

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Selected Response Item - Released in 2002

Sue is scheduled to take a biology test at school today. To perform well on the test, she knows it is best to eat a breakfast with a high ratio of carbohydrates to serving size.

Which of these foods has the highest ratio of carbohydrates to serving size?

  1. Bagel
  2. Milkshake
  3. Raisins
  4. Wheat cereal
/share/clg/xml/public_release/mathematics/2002_321_alg20.xml

Correct Answer:
D

Selected Response Item - Released in 2002

The spinner shown below is spun 20 times.

The results of the spins are shown below.

Based on these results, how many times would 2 be expected to appear in 60 spins?

  1. 8
  2. 15
  3. 24
  4. 28
/share/clg/xml/public_release/mathematics/2002_321_alg24.xml

Correct Answer:
C

Selected Response Item - Released in 2005

Karen spun a spinner 50 times and recorded her results in the table below. The spinner had five numbered sections.

Based on the results in the table, how many times should Karen expect the spinner to land on section 3 or 4 if she spins the spinner 300 times?

  1. 60
  2. 72
  3. 108
  4. 132
/share/clg/xml/public_release/mathematics/2005_321_alg11.xml

Correct Answer:
D

Extended Constructed Response (ECR) Item - Released in 2005

Paul asked 50 randomly selected eleventh-grade students to choose their favorite candidate for class president. The survey results are shown in the table below.

Complete the following in the Answer Book:

  • There are 300 eleventh-grade students at Paul's school. Based on the survey results, how many votes will Marie expect to receive? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • Using the survey results, Paul claims that Bertha will receive 2 more votes than Nick in the election. Is Paul correct? Use mathematics to justify your answer.
  • Loren asked the same question in another survey. She asked 50 randomly selected eleventh-grade chorus students to choose their favorite candidate for class president. Will you expect Loren's survey or Paul's survey to give more reliable results? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2005_321_alg30.xml

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Selected Response Item - Released in 2005

A student at West High School conducted a random survey of 200 tenth-grade students to determine their favorite season. The survey results are shown in the table below.

There are 500 tenth-grade students in the school. Based on the survey results, how many of these tenth-grade students would be expected to choose Spring as their favorite season?

  1. 105
  2. 125
  3. 130
  4. 160
/share/clg/xml/public_release/mathematics/2005_321_alg32.xml

Correct Answer:
D

Selected Response Item - Released in 2001

A television producer wants to broadcast a new program for young children. The table below shows information on the average daily television viewing time for two age groups of children.
Based on the data in the table, which time period would be the best choice for the new television program for 2- to 5-year-olds?

  1. 7 to 10 a.m.
  2. 10 a.m. to 1 p.m.
  3. 4 to 7 p.m.
  4. 7 to 10 p.m.
/share/clg/xml/public_release/mathematics/2001_321_alg12.xml

Correct Answer:
A

Selected Response Item - Released in 2003

Mr. Shin wants to order notebooks for the school store. Notebooks come in four colors: red, blue, green, and black. He randomly surveyed 50 students to determine which color notebook they would buy. The table below shows the results.

Mr. Shin will order 400 notebooks. How many blue notebooks should he order?

  1. 22
  2. 88
  3. 176
  4. 200
/share/clg/xml/public_release/mathematics/2003_321_alg20.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2003

Juan conducted two different surveys about student transportation to school. For Survey A, he stood at the entrance of the school at 7:30 a.m. and surveyed the first 80 students. For Survey B, he used a random number generator to select 80 students in the school to survey. His results are shown in the tables below.

Complete the following in the answer box below:
  • Use principles of simple random sampling to justify why Juan should have more confidence in the results of Survey B.
     
  • Use principles of simple random sampling to justify why Juan should have less confidence in the results of Survey A.
     
  • According to the data collected from Survey B, of the 400 total students in the school, how many students should Juan expect to ride a bike? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
     

/share/clg/xml/public_release/mathematics/2003_321_alg21.xml

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Extended Constructed Response (ECR) Item - Released in 2004

A city bus company requires exact change or a token to ride a bus. The company conducted a random survey of 100 passengers to determine how they paid their bus fare. The survey results are shown in the table below.

Complete the following in the answer box below:
  • Last week 2,000 passengers rode the bus. Based on this survey, how many of these passengers would be expected to use exact change to pay the bus fare? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
     
  • Mr. Blake, a bus driver for the city bus company, reported that 44 passengers who rode on his bus one morning paid using a token. Based on this survey, estimate how many passengers rode on his bus that morning. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
     
  • Should a different city use these survey results to predict the number of bus passengers that would be expected to use exact change to ride the bus in their city? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2004_321_alg11.xml

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Selected Response Item - Released in 2004

The mayor of a town conducted an opinion survey of 90 randomly selected voters. The mayor wants to determine if a new shopping mall should be built in town. The survey results are shown in the table below.

There are 1,440 voters in the town. How many voters would be expected to want the new shopping mall built?

  1. 160
  2. 320
  3. 860
  4. 960
/share/clg/xml/public_release/mathematics/2004_321_alg17.xml

Correct Answer:
D

Selected Response Item - Released in 2004

One hundred randomly selected students from Western High School were surveyed to determine whether they would like school to start one hour later. Of the students surveyed, 58 favored the change. Western High School has 1,200 students. According to the survey results, which of these is a reasonable prediction of the total number of students who would favor this change?

  1. 42
  2. 58
  3. 504
  4. 696
/share/clg/xml/public_release/mathematics/2004_321_alg20.xml

Correct Answer:
D

Selected Response Item - Released in 2003

A quality-control expert for a key manufacturer examined the keys produced by a particular machine. The table below shows the number of defective keys found in the 8 groups of 100 keys he examined.

How many defective keys would be expected in a group of 5,000 keys? Round the answer to the nearest whole number.

  1. 150
  2. 170
  3. 213
  4. 243
/share/clg/xml/public_release/mathematics/2003_321_alg29.xml

Correct Answer:
C

Selected Response Item - Released in 2006

The table below shows the possible scores for a game and the number of times each score occurred.

Using the information in the table, predict how many times a score of "7" would occur in 100 tries.

  1. 12
  2. 15
  3. 18
  4. 22
/share/clg/xml/public_release/mathematics/2006_321_alg09.xml

Correct Answer:
B

Selected Response Item - Released in 2006

A store owner surveyed customers to determine color preferences of bathroom tile. The results of the survey are shown below.

Which of these is the best conclusion based on the results of the survey?

  1. The store owner should only order white tile.
  2. The store owner should only order beige and pink tile.
  3. The store owner should order more cases of beige and white tile than any other color.
  4. The store owner should order more cases of yellow and teal tile than any other color.
/share/clg/xml/public_release/mathematics/2006_321_alg10.xml

Correct Answer:
C

Selected Response Item - Released in 2007

The table below shows the percent of golfers who participate in other activities.

Based on the table, out of 50 golfers, how many would be expected to watch sports on TV?

  1. 16 golfers
  2. 29 golfers
  3. 33 golfers
  4. 58 golfers
/share/clg/xml/public_release/mathematics/2007_321_alg03.xml

Correct Answer:
B

Selected Response Item - Released in 2007

In a small town, 250 randomly sampled registered voters were asked to state whether they would vote “Yes” or “No” on Measure A in the next local election. The table below shows the results of the survey.

There are 5,500 people expected to vote in the next election. Based on the data, how many people will vote “No” on Measure A in the next election?

  1. 96
  2. 130
  3. 2,112
  4. 5,280
/share/clg/xml/public_release/mathematics/2007_321_alg37.xml

Correct Answer:
C
Resources for 3.2.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |