unit 9 probability and statistics homework 8 answer key

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Statistics and probability

Unit 1: analyzing categorical data, unit 2: displaying and comparing quantitative data, unit 3: summarizing quantitative data, unit 4: modeling data distributions, unit 5: exploring bivariate numerical data, unit 6: study design, unit 7: probability, unit 8: counting, permutations, and combinations, unit 9: random variables, unit 10: sampling distributions, unit 11: confidence intervals, unit 12: significance tests (hypothesis testing), unit 13: two-sample inference for the difference between groups, unit 14: inference for categorical data (chi-square tests), unit 15: advanced regression (inference and transforming), unit 16: analysis of variance (anova).

Curriculum  /  Math  /  7th Grade  /  Unit 8: Probability  /  Lesson 8

Probability

Lesson 8 of 9

Criteria for Success

Anchor problems, problem set, target task, additional practice.

Determine the probability of compound events.

Common Core Standards

Core standards.

The core standards covered in this lesson

Statistics and Probability

7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Determine the sample space for a compound event and use lists, tables, or tree diagrams as needed to organize the sample space.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

A fair six-sided die is rolled twice. What is the theoretical probability that the first number that comes up is greater than or equal to the second number?

Guiding Questions

Rolling Twice , accessed on June 14, 2017, 2:49 p.m., is licensed by Illustrative Mathematics under either the  CC BY 4.0  or  CC BY-NC-SA 4.0 . For further information, contact Illustrative Mathematics .

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the theoretical probability that Angie and Carlos are seated opposite each other?

Sitting Across from Each Other , accessed on June 14, 2017, 2:40 p.m., is licensed by Illustrative Mathematics under either the  CC BY 4.0  or  CC BY-NC-SA 4.0 . For further information, contact Illustrative Mathematics .

A standard deck of playing cards includes 52 cards, equally divided among 4 suits: hearts, diamonds, clubs, and spades.

You have two standard decks of cards. You draw a card from the first deck, record the suit, and then draw a card from the second deck and record the suit.

a.   What is the probability that you draw a heart and a diamond, in that order?

b.   What is the probability that you draw a heart and a diamond, in any order?

A set of suggested resources or problem types that teachers can turn into a problem set

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Lin plays a game that involves a standard number cube and a spinner with four equal sections numbered 1 through 4. If both the cube and spin result in the same number, Lin gets another turn. Otherwise, play continues with the next player. What is the probability that Lin gets another turn?

Grade 7 Unit 8 Lesson 9 Teacher Version is made available by Open Up Resources  under the  CC BY 4.0  license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed April 5, 2018, 1:13 p.m..

Student Response

An example response to the Target Task at the level of detail expected of the students.

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• MARS Summative Assessment Tasks for Middle School Memory Game
• Illustrative Mathematics Red, Green, or Blue? — (Note: this is a challenging problem that would be a good problem for students to do in pairs)
• Open Up Resources Grade 7 Unit 8 Practice Problems — Lesson 9

Topic A: Probability Models of Simple Events

Understand the probability of an event happening is a number between 0 and 1, ranging from impossible to certain.

Define probability and sample space. Estimate probabilities from experimental data.

7.SP.C.6 7.SP.C.7

Determine the probability of events.

7.SP.C.7.A 7.SP.C.7.B

Use probability to predict long-run frequencies.

Design and conduct simulations to model real-world situations.

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Topic B: Probability Models of Compound Events

Conduct simulations with multiple events to determine probabilities.

7.SP.C.8 7.SP.C.8.C

List the sample space for compound events using organized lists, tables, or tree diagrams.

Design and conduct simulations to model real-world situations for compound events.

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mean = 4 hours, standard deviation = 1.2 hours, sample size = 16

a. Check student's solution. b. 3.5, 4.25, 0.2441

The fact that the two distributions are different accounts for the different probabilities.

The sample size, n , gets larger.

• U (24, 26), 25, 0.5774
• N (25, 0.0577)
• N (2500, 5.7735)

N ( 10,  10 8 ) ( 10,  10 8 )

• Χ = amount of change students carry
• Χ ~ Exp (1/0.88) or approximately Χ ~ Exp (1.1364)
• X ¯ X ¯ = average amount of change carried by a sample of 25 students.
• X ¯ X ¯ ~ N (0.88, 0.176)
• The probability in part (e) represents the probability of an individual value. In part (f), the probability describes the mean of a sample of 25. Part (f) relies on the central limit theorem, so the distributions are different. Part (e) is exponential and part (f) is normal.
• length of time for an individual to complete IRS form 1040, in hours
• mean length of time for a sample of 36 taxpayers to complete IRS form 1040, in hours
• N ( 10 .53,  1 3 ) ( 10 .53,  1 3 )
• Yes, I would be surprised, because the probability is almost 0.
• No, I would not be totally surprised because the probability is 0.2312.
• the length of a song, in minutes, in the collection
• the average length, in minutes, of the songs from a sample of five albums from the collection
• N (2.75, 0.0220)
• 2.74 minutes
• 0.03 minutes
• True. The mean of a sampling distribution of the means is approximately the mean of the data distribution.
• True. According to the central limit theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.
• The standard deviation of the sampling distribution of the means will decrease, making it approximately the same as the standard deviation of X as the sample size increases.
• X = the yearly income of someone in a Third World country
• the average salary from samples of 1,000 residents of a Third World country
• X ¯ X ¯ ∼ N ( 2,000,  8,000 1,000 ) ( 2,000,  8,000 1,000 )
• Very wide differences in data values can have averages smaller than standard deviations.
• The distribution of the sample mean will have higher probabilities closer to the population mean. P (2,000 < X ¯ X ¯ < 2,100) = 0.1537 P (2,100 < X ¯ X ¯ < 2,200) = 0.1317
• the total length of time for nine criminal trials
• N (189, 21)
• 162.09; 90 percent of the total nine trials of this type will last 162 days or more.
• X = the salary of one elementary school teacher in the district
• X ~ N (44000, 6500)
• ΣX ~ sum of the salaries of 10 elementary school teachers in the sample
• ΣX ~ N (44,000, 20,554.80)
• Sampling 70 teachers instead of 10 would cause the distribution to be more spread out. It would be a more symmetrical normal curve.
• If every teacher received a $3,000 raise, the distribution of X would shift to the right by $3,000. In other words, it would have a mean of $47,000.
• X = the closing stock prices for U.S. semiconductor manufacturers
• i. $20.71, ii. $17.31, iii. 35
• exponential distribution, Χ ~ Exp ( 1 20.71 ) ( 1 20.71 )
• Answers will vary.
• i. $20.71, ii. $11.14
• N ( 20 .71,  17.31 5 ) ( 20 .71,  17.31 5 )
• Check student’s solution.
• X ¯ X ¯ ~ N ( 60,  9 25 ) ( 60,  9 25 )
• N (1500, 45)
• We have μ = 17, σ = 0.8, x ¯ x ¯ = 16.7, and n = 30. To calculate the probability, we use normalcdf (lower, upper, μ , σ n σ n ) = normalcdf ( E – 99,16 .7,17, 0. 8 30 ) ( E – 99,16 .7,17, 0. 8 30 ) = 0.0200.
• If the process is working properly, then the probability that a sample of 30 batteries would have at most 16.7 life span hours is only 2%. Therefore, the class was justified to question the claim.
• For the sample, we have n = 100, x ¯ x ¯ = 0.862, and s = 0.05.
• Σ x ¯ Σ x ¯ = 85.65, Σs = 5.18
• normalcdf (396.9, E 99,(465)(0.8565),(0.05)( 465 465 )) ≈ 1
• Because the probability of a sample of size of 465 having at least a mean sum of 396.9 is appproximately 1, we can conclude that the company is correctly labeling their candy packages.

Use normalcdf ( E – 99,1 .1,1, 1 70 ) ( E – 99,1 .1,1, 1 70 ) = 0.7986. This means that there is an 80 percent chance that the service time will be less than 1.1 hours. It may be wise to schedule more time because there is an associated 20 percent chance that the maintenance time will be greater than 1.1 hours.

Because we have normalcdf ( 5. 111,5 .291,5 .201, 0. 065 280 ) ( 5. 111,5 .291,5 .201, 0. 065 280 ) ≈ 1, we can conclude that practically all the coins are within the limits; therefore, there should be no rejected coins out of a well-selected sample size of 280.

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Browse Course Material

Course info, instructors.

• Dr. Jeremy Orloff
• Dr. Jennifer French Kamrin

Departments

• Mathematics

As Taught In

• Discrete Mathematics
• Probability and Statistics

Learning Resource Types

Introduction to probability and statistics, exams with solutions.

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All Things Algebra®

Math 7 Unit 8: Probability & Statistics

This unit includes 59 pages of guided notes, homework assignments, three quizzes, a study guide, and a unit test that cover the topics listed in the description below.

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This unit contains the following topics:

• Outcomes and Events • Theoretical Probability (Simple Events) • Theoretical vs. Experimental Probability • Tree Diagrams • Fundamental Counting Principle • Compound Probability (independent events only) • Populations and Samples • Biased vs. Unbiased Samples • Using Sampling to Predict • Measures of Center: Mean, Median, and Mode • Range • Stem-and-Leaf Plots • Histograms • Box-and-Whisker Plots

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Description

This Probability and Statistics Unit Bundle includes guided notes, homework assignments, three quizzes, a study guide, a unit test, and more that cover the following topics:

• Simple Probability

• Theoretical vs. Experimental Probability

• Counting Outcomes

• Tree Diagrams

• Fundamental Counting Principle

• Compound Probability; Independent vs. Dependent Events

• Probability with Replacement and Non-Replacement

• Populations vs. Samples

• Biased vs. Unbiased Samples

• Using Samples to Predict

• Measures of Central Tendency: Mean, Median, and Mode

• Mean Absolute Deviation

• Box-and-Whisker Plots

• Scatter Plots

• Line of Best Fit

• Two-Way Tables

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