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Algebra IIData and Probability

PART 1 – Data Day Topic(s) In class Assignment Done?1 Histograms; Stem and

leaf; Shape of dataNotes (handout)

15.1 Worksheet

2 Box and whisker plots; Shape of data

Notes/Fruit Loop Activity (handout)

15.2 Worksheet

3 Scatter plots; Correlation; Outliers

Stations 15.3 Worksheet

4 Transforming data Investigation 15.4 Worksheet

PART 2 – Probability Day Topic(s) In class Assignment Done?5 The counting principal Quiz over Pt 1

Investigation15.5 Worksheet

6 Permutations Notes (handout)

p486/ 1 – 6, 16, 186.1 on syllabus

7 Combinations Notes (handout)

p486/ 7, 8, 17, 19 – 23 7.1 syllabus

8 Probability; Probability distributions

Notes (handout)

15.8 Worksheet

9 Compound probability Jigsaw; Notes (handout)

15.9 Worksheet

10 Probability mélange Marker boards 15.10 Worksheet11 Review WORK! Review12 Assessment Test

6.1 Write 3 sentences comparing the two distributions. “Dotplots” can be interpreted the same way as histograms.

7.1

Correlation direction: _______________________________________________________________________Potential outlier(s): _________________________________________________________________________Description: ________________________________________________________________________________________________________________________________________________________________________

Algebra II Name: ______________________________15.1 Worksheet

1. The histogram shows the number of major hurricanes that reached the East Coast of the United States from 1944 to 2005.

(a) What does the height (↑) of each bar represent?

(b) What does the width (↔) of each bar represent?

(c) What can you say about the median?

(d) What can you say about the mode?

(e) What can you say about the range?

(f) Describe the shape IN CONTEXT.

2. Answer the following questions regarding the histogram below. It shows the distribution of electoral votes for the 50 United States and the District of Columbia.







3. Make a frequency table and histogram with the following data set. Don’t forget to label!

Class Limits Tally Frequency10 – 14

50 – 54 (a) What does the height (↑) of each bar (b) What does the width (↔) of each bar represent? represent?

(c) What is the median? (d) What is the mode?

(e) What is the range? (f) Describe the shape.

4. Make a stemplot and answer the questions. Don’t forget a key!

(a) What is the median?

(b) What is the mode?

(c) What is the range?

(d) Describe the shape.

Stem Leaf


1. Find the five number summary and construct a box plot for the following data.Consumer Reports did a study of ice cream bars. 27 bars with taste ratings of at least “fair” were listed, and cost per bar was in the article. As you can see, the cost varies quite a bit, partly because the bars are not of uniform size. (HINT: The data is already ordered for you!)

0.16 0.17 0.18 0.20 0.25 0.33 0.33 0.35 0.370.38 0.40 0.47 0.50 0.50 0.50 0.63 0.84 0.970.97 0.99 1.00 1.03 1.07 1.07 1.07 1.08 1.23

Use the following box plot to answer questions 2 – 5.

2. Which distribution (males or females) has a larger range? Calculate both.

3. Which distribution (males or females) has a larger interquartile range? Calculate both.

4. Mark the truth or falsity for each statement in the chart. Three statements are true.Statement True False Not enough

information to determine

The heaviest female weighs the same as the average male.The mode for female weight is between 111 and 128 pounds.The maximum male weight is 235 pounds.The heaviest 50% of males are heavier than all females.No male weighs exactly 160 pounds.The person with the lowest weight is a male.The heaviest person in the class is a male.

5. Which of the following is not correct? Circle only one.

6.

7. Describe the shape of the distribution in the stem plot in number 6 in a complete sentence.

8. Write three full sentences comparing the following distributions.


For questions 1 – 4, describe the shape of the correlation (positive, negative or no) and identify any potential outliers as an ordered pair (x, y). Write one sentence describing the relationship between the variables graphed. Use the lines on the back of this sheet.

1. 2.

3. 4.

1. Correlation direction: _____________________________________________________________________Potential outlier(s): _________________________________________________________________________Description: ________________________________________________________________________________________________________________________________________________________________________




5.

6. Sketch an example of a histogram with the given shape.(a) Bimodal (b) Skewed left (c) Bell curve (d) Symmetric (e) Uniform


1. Summary statistics for a college level biology course are given below. Suppose the professor curves the test by adding 8 points to each score. Fill in the new summary statistics in the chart.

Mean Median Mode Range

Old (original) 65.2 72.5 71 58

New (curved)

2. Summary statistics for a psychology quiz are given below. The quiz was worth 50 points, but the professor wants to record a grade out of 100 points, so she multiples all of the scores by 2. Fill in the new summary statistics in the chart.


Old (50 pts) 41 35 42 39

New (100 pts)

3. Mrs. Crazypants measured the heights of her 16 children in inches last Saturday. Today, she realized her measuring tape was missing the first 2 inches, so all of her measurements were 2 inches short, so she must add these two inches back to each measurement to be correct. Fill in the new summary statistics in the chart.


Old 48 48 No mode 34

New

4. Summary statistics for the daily average temperature in Awesometown are given below in degrees

Fahrenheit. The formula to convert Fahrenheit to Celsius is C=59(F−32). Fill in the new summary statistics

in the chart.Mean Median Mode Minimum Maximum Range

Old (⁰F) 52 55 62 11 101 90

New (⁰C)

5. Find the five-number summary (Min, Q1, Med, Q3, Max) and construct a box plot. The data below is the number of unprovoked attacks by alligators on people in Florida each year for a 33-year period.

1 2 3 3 4 4 5 5 5 6 6 6 6 69 9 9 10 11 12 13 13 14 14 14 15 17 1717 18 20 22 24

6. Describe the shape of the correlation (positive, negative or no) and identify any potential outliers as an ordered pair (x, y). Write one sentence describing the relationship between the variables graphed.

Correlation direction: _______________________________________________________________________Potential outlier(s): _________________________________________________________________________Description: ________________________________________________________________________________________________________________________________________________________________________

Use the following data set for questions 7 – 8.

7. Make a stem plot of these data. Don’t forget a key!

8. Suppose we convert the times to HOURS from minutes by dividing by 60. The current statistics are given in the chart. Calculate the NEW statistics in hours.

Statistic Old (minutes) New (hours)Mean 144.68

Minimum 96Q1 116.5

Median 139Q3 170

Maximum 207IQR 53.5

Range 111


For questions 1 – 6, assume that you draw three cards from a standard deck, REPLACING each card before drawing the next. Find the number of ways there are to draw three cards in a row, fitting the requirements specified.

1. face card, face card, face card 2. heart, diamond, spade

3. jack, queen, king 4. jack, jack, jack

5. black 10, red 10, any 10 6. ace, two, three

For questions 7 – 12, assume that you draw three cards from a standard deck, WITHOUT REPLACING each card before drawing the next. Find the number of ways there are to draw three cards in a row, fitting the requirements specified.

7. face card, face card, face card 8. heart, diamond, spade

9. jack, queen, king 10. jack, jack, jack

11. black 10, red 10, any 10 12. ace, two, three

13. How many 3-digit positive odd integers can be formed from the digits 1, 2, 5, 6 and 7?

14. How many license plates can be made with the structure letter-letter-letter-digit-digit-digit (allow for repetitions)?

15. How many license plates can be made with the structure letter-letter-letter-digit-digit-digit (without repetitions)?

16. How many license plates can be made with the structure letter-digit-letter-letter-digit-letter (without repetitions)?

17. How many outcomes are possible if you roll 2 dice?

18. How many outcomes are possible if you roll 3 dice and flip a coin?

19. Answer the questions about the histogram.








Convert the following probability to a percent.

1. p = 0.4 2. p=35 3. p=

215

5.2 Convert the following to a decimal.

4. p = 45.6% 5. p = 90% 6. p=1120

Fill out the probability for each outcome as a decimal (round to the nearest hundredth). Graph the probability distribution (histogram).7. You flip a coin twice.

Outcome Both heads

One of each Both tails

P(outcome)

8. You roll a weighted die. It’s probability distribution is given below. Graph the probability distribution and answer the questions. (Some may have the same answer.)

Outcome 1 2 3 4 5 6

P(outcome)14

14

14

112

112

112

(a) Find P(more than 3)

(b) Find P(at least 3)

(c) Find P(no more than 3)

1 2 3 4 5 6(d) Find P(at most 3)

(e) Find P(no less than 3)

Number of “tails”

0 1 2

Prob

abili

ty

Outcome

Prob

abili

ty

(f) Find P(not 3)


Use the Venn diagram below for questions 1 – 6. Lowercase letters represent outcomes. All outcomes are equally likely. Capital letters represent events.

1. Find P(A∩B)

2. Find P(A∪B)

3. Find P(D)

4. Find P(B∪C∪D)

5. Find P(A∩B∩C)

6. Find P(C∩D)

Draw a Venn diagram and label with the appropriate probabilities based on the description given. All situations involve two events: A and B.

7. A and B are mutually exclusive. 8. P (A )=0.50 ; P (B )=0.25 ; P (A∩B )=0.10P (A )=0.25 ; P (B )=0.3

9. P (A )=0.4 ;P (B )=0.1; P ( A∪B )=0.35

Answer the questions about probability and percents using the appropriate formula.

10. You roll two dice. What is the probability that the sum will be 12?

11. You flip three coins. What is the probability that all three will show “tails”?

12. A hockey team played 52% of their games at home this season. They won 80% of their home games and 65% of their away games. What percent of their games did they win this season?

13. The probability that you will drop your phone the next time you take it out of your pocket is 8%. What is the probability that you will not drop it?

bh e c jfi k a g d

l

A B

D

C

14. The probability that it will rain in Chicago is 70%. The probability that it will rain in London is 85%. What is the probability that it will not rain in either city.

15. The probability that Gary will eat breakfast tomorrow is 0.6. The probability that he will eat lunch is 0.89. The probability that he will have both meals is 0.72. What is the probability that he will eat breakfast or lunch?

16. You roll a weighted die. It’s probability distribution is given below. Graph the probability distribution and answer the questions. (Some may have the same answer.)

Outcome 1 2 3 4 5 6

P(outcome)14

112

112

112

14

14

(a) Find P(more than 3)

(b) Find P(at least 3)

(c) Find P(no more than 3)

1 2 3 4 5 6(d) Find P(at most 3)

(e) Find P(no less than 3)

(f) Find P(not 3)

For questions 17 – 20, assume that you draw three cards from a standard deck, WITHOUT REPLACING each card before drawing the next. Find the number of ways there are to draw three cards in a row, fitting the requirements specified.

17. face card, 10, face card 18. ace, ace, ace

19. heart, heart, heart 20. red queen, black queen, any queen

Outcome

Prob

abili

ty


1. Each of the letters in the word SQUARE is written on a different card, and the six cards are shuffled. One card is drawn at random.

(a) What is the sample space?

(b) Specify the event “the card drawn is a vowel”?

2. Evaluate.

(a) 6 ! (b) 7 !3! 4 ! (c) 4C2 (d) 10C3

3. If a six-volume set of books is placed on a shelf at random, what is the probability that the books will be arranged in either correct or reverse order? (fraction, decimal)

4. The probability that project Alpha will succeed is 60%, that project Beta will succeed is 45% and that project Gamma will succeed is 70%. Find the probability that all three projects fail (assume all are independent). (percent)

5. From a choice of 5 novels and 5 biographies, 3 books are selected. What is the probability that at least 2 are novels? (fraction, decimal)

6. At Bayside High School, 55% of the student body are boys. Thirty-five percent of the boys are on honor roll and 40% of the girls are on honor roll. What percent of the student body is on honor roll? Round to the nearest percent.

7. Mrs. Brown gives two tests to her class. 30% of the class passed both tests and 45% passed the first test. What percent of those who passed the first test also passed the second test?

8. There are 3 red, 2 blue and 3 yellow crayons in a box. Two are drawn at random. What is the probability that BOTH crayons will be blue… (fractions)

(a) … the first is replaced before drawing the second?

(b) … if the first is NOT replaced before drawing the second?

9. How many ways can the letters of “SOME” be arranged?

10. How many ways can the letters of “NONE” be arranged?

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