Skills Practice Skills Practice for Lesson 17.1

Transcription

1 Skills Practice Skills Practice for Lesson.1 Name Date Products and Probabilities Discrete Data and Probability Distributions Vocabulary Describe similarities and differences between each pair of terms. 1. discrete data and continuous data 2. probability distribution and probability histogram 3. experimental probability and theoretical probability Chapter l Skills Practice 10

2 Provide an example and an explanation of the term. 4. relative frequency table Problem Set State whether each is an example of discrete data or continuous data. 1. depth of snow continuous data 2. distance a bird flies 3. number of box cars on a freight train 4. squares in a crossword puzzle 5. text messages Matt sent yesterday 6. volume of air in a balloon 1018 Chapter l Skills Practice

3 Name Date Complete the relative frequency table for each set of data. 7. Rebecca measured how far each third grader could throw a ball. The distances in feet were 22, 22, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, and 30. Distance (feet) Number of Occurrences Relative Frequency Danielle scored the following number of points in the basketball games she played this year: 0, 0, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 12, 12, 12, and 15. Number of Points Number of Games Relative Frequency Chapter l Skills Practice 1019

4 9. The table shows the high temperature in Central City on January 1st for the past forty years. Temperature Number of Years Temperature Number of Occurrences Relative Frequency Chapter l Skills Practice

5 Name Date 10. Cristian rolled a number cube 50 times. It displayed 1 five times, 2 nine times, 3 sixteen 16 times, 4 thirteen times, 5 four times, and 6 three times. Number Number of Occurrences Relative Frequency The table shows the lengths of the fish caught in the Sandy River this year. Length (inches) Number of Fish Length (inches) Number of Occurrences Relative Frequency Chapter l Skills Practice 1021

6 12. Abby asked her classmates how many songs they have on their MP3 players. Four said 25, twelve said 50, twenty said 75, nineteen said 100, and twenty-five said 125. Number of Songs Number of Occurrences Relative Frequency Create a probability histogram for each relative frequency table. 13. Quiz Score Number of Occurrences Relative Frequency Probability Quiz Scores Score 1022 Chapter l Skills Practice

7 Name Date 14. Age of Child Number of Occurrences Relative Frequency Chapter l Skills Practice 1023

8 15. Tae Kwon Do Score Number of Occurrences Relative Frequency Chapter l Skills Practice

9 Name Date 16. Month Number of Weddings Relative Frequency March April May June July August Chapter l Skills Practice 1025

10 . Number of Golf Strokes to Hole Number of Occurrences Relative Frequency Chapter l Skills Practice

11 Name Date 18. Tax Returns Done in a Day Number of Occurrences Relative Frequency Chapter l Skills Practice 1027

12 Calculate each probability. 19. Calculate the probability of a quiz score being at least 4. Quiz Score Number of Occurrences Relative Frequency Calculate the probability that the age of a child was less than 3. Age of Child Number of Occurrences Relative Frequency Calculate the probability that the score was even. Tae Kwon Do Score Number of Occurrences Relative Frequency Chapter l Skills Practice

13 Name Date 22. Calculate the probability that a wedding was in June or July. Month Number of Weddings Relative Frequency March April May June July August Calculate the probability that the number of golf strokes was odd. Number of Golf Strokes to Hole Number of Occurrences Relative Frequency Calculate the probability that at least 4 returns were done in a day. Tax Returns Done in a Day Number of Occurrences Relative Frequency Chapter l Skills Practice 1029

14 The relative frequency table summarizes the possible sums when rolling two number cubes. Use theoretical probabilities to make each prediction. Sum of Numbers Displayed Number of Occurrences on Two Number Cubes 2 1 Relative Frequency If two number cubes are rolled 20 times, how many times will the displayed sum be 4? The theoretical probability of rolling a sum of 4 is So, if two number cubes are rolled 20 times, then the sum will be 4 approximately (20) 1.666, or about 2 times. 26. If two number cubes are rolled 50 times, how many times will the displayed sum be 8? 27. If two number cubes are rolled 60 times, how many times will the displayed sum be greater than or equal to 7? 1030 Chapter l Skills Practice

15 Name Date 28. If two number cubes are rolled 72 times, how many times will the displayed sum be less than 4? 29. If two number cubes are rolled 250 times, how many times will the displayed sum be an odd number? 30. If two number cubes are rolled 400 times, how many times will the displayed sum be a multiple of 3? The relative frequency table summarizes the possible outcomes for families with four children. Use theoretical probabilities to make each prediction. Families with Four Children 4 Boys Relative Frequency Boys and 1 Girl Boys and 2 Girls Boy and 3 Girls Girl If twenty families each have 4 children, how many of these families have 3 girls and 1 boy? The theoretical probability of having 3 girls and 1 boy is So, if twenty families are considered, then there will be 0.25(20) 5 families with 3 girls and 1 boy. Chapter l Skills Practice 1031

16 32. If fifty families each have 4 children, how many of these families have 2 girls and 2 boys? 33. If one hundred families each have 4 children, how many of these families have all boys? 34. If two hundred twenty families each have 4 children, how many of these families have all girls? 35. If one thousand families each have 4 children, how many of these families have at least 2 boys? 36. If two thousand families each have 4 children, how many of these families have no more than 1 girl? 1032 Chapter l Skills Practice

17 Skills Practice Skills Practice for Lesson.2 Name Date Basketball and Blood Type The Binomial Probability Distribution Vocabulary Write the term that best completes each statement. 1. A(n) is a probability that collects or adds several probabilities. 2. The describes probabilities for outcomes of multiple trials of binomial experiments. 3. An experiment that satisfies the conditions that there are a fixed number of trials, each trial is independent from every other trial, each trial has two mutually exclusive outcomes, and the probability of success is the same for each trial is called a(an), Problem Set Determine whether each experiment is a binomial experiment. If it is not, explain why not. 1. A coin is tossed and the number of times it lands heads is recorded. The experiment is a binomial experiment. 2. A random sample of students is taken and the color of their hair is recorded. 3. A random sample of students is taken and the number who are color blind is recorded. 4. A random sample of people in the United States is taken and the number of children they have is recorded. Chapter l Skills Practice 1033

18 5. A random sample of students is taken and the name of the person they are planning to vote for Homecoming Queen is recorded. 6. A random sample of bowlers is taken and the number who have ever bowled a perfect score is recorded. For each binomial experiment, identify the number of trials n, the possible outcomes, the probability of success p, and the probability of failure 1 p. 7. A random sample of 10 people in the United States is taken and the number that are age 65 or older is recorded. (According to the 2000 census, 12.4% of the population was age 65 or older.) The number of trials is 10, so n 10. The outcomes are being age 65 or older or not being that old. The probability of success is p The probability of failure is 1 p Two number cubes are rolled 20 times and the number of times the sum of the numbers displayed is 3 is recorded. 9. Robbie s batting average is 0.300, which means he gets a hit 30% of the time he bats. Robbie bats 20 times this week and the number of times he gets a hit is recorded. 10. A random sample of 10 students at the University of Georgia is selected and the number of male students is recorded. (In 2008, 42% of the students enrolled at the University of Georgia were male.) 11. One number cube is rolled 50 times and the number of times an even number is rolled is recorded Chapter l Skills Practice

19 Name Date 12. Two coins are tossed 30 times and the number of times both land on heads is recorded. Complete each table to define a binomial probability distribution. 13. A coin is tossed twice and the number of times it lands on heads is recorded. Number of Heads Probability The number of people age 65 or older in a sample of 3 people is recorded. (According to the 2000 census, 12.4% of the population was age 65 or older.) Number Age 65 or Older Probability 15. The number of hits Robbie gets if he bats 3 times is recorded. Robbie s batting average is 0.300, which means he gets a hit 30% of the time he bats. Number of Hits Probability 16. The number of times a number cube shows 4 if it is rolled twice is recorded. Number of Times Four Occurs Probability Three University of Georgia students are selected, and the number of males is recorded. (In 2008, 42% of the students enrolled at the University of Georgia were male.) Number of Males Probability Chapter l Skills Practice 1035

20 18. Central College wins 62% of their lacrosse games. They play 3 games, and the number of games won is recorded. Number of Games Won Probability Calculate each probability. 19. According to the 2000 census, 12.4% of the population was age 65 or older. In a sample of 20 people, what is the probability that exactly 3 people are age 65 or older? 20 C 3 (0.124)3 (0.876) ! 3!(20 3)! (0.124)3 (0.876) Suppose that 16% of the population of a town is age 65 or older. In a sample of 50 people, what is the probability that exactly 10 people are age 65 or older? 21. Suppose that 8% of the population in a country is age 65 or older. In a sample of 50 people, what is the probability that either 9 or 10 of them are age 65 or older? 22. Robbie s batting average is 0.300, which means he gets a hit 30% of the time he bats. What is the probability that Robbie gets 5 hits in his next 12 at bats? 1036 Chapter l Skills Practice

21 Name Date 23. Suzanne s batting average is 0.270, which means she gets a hit 27% of the time she bats. What is the probability that Suzanne gets at least 5 hits in her next 6 at bats? 24. In 2008, 42% of the students enrolled at the University of Georgia were male. What is the probability that exactly 10 of 20 randomly selected students at the University of Georgia are male? Determine whether each probability is an example of cumulative probability. 25. The probability that Robbie gets 5 hits in 8 at bats; Robbie s batting average is 0.300, which means he gets a hit 30% of the time he bats. not cumulative probability 26. The probability that Suzanne gets more than 5 hits in 8 at bats; Suzanne s batting average is 0.270, which means she gets a hit 27% of the time she bats. 27. The probability that Randall gets at least 5 hits in 8 at bats; Randall s batting average is 0.345, which means he gets a hit 34.5% of the time he bats. 28. The probability that exactly 100 of 250 randomly selected people are age 65 or older. (According to the 2000 census, 12.4% of the population was age 65 or older.) 29. The probability that more than 12 of 20 randomly selected people from a town are age 65 or older. (16% of the town s population is age 65 or older.) Chapter l Skills Practice 1037

22 30. The probability that less than 12 of 30 randomly selected people from a country are age 65 or older. (8% of the country s population is age 65 or older.) Calculate each probability using a graphing calculator. 31. The probability that Robbie gets 30 hits in his next 60 at bats. Robbie s batting average is 0.300, which means he gets a hit 30% of the time he bats. P(30) , or about 0.05% 32. The probability that Robbie gets less than 9 hits in his next 15 at bats. Robbie s batting average is 0.300, which means he gets a hit 30% of the time he bats. 33. The probability that Robbie gets at least 9 hits in his next 15 at bats. Robbie s batting average is 0.300, which means he gets a hit 30% of the time he bats. 34. The probability that 30 of 250 randomly selected people are age 65 or older. According to the 2000 census, 12.4% of the population was age 65 or older. 35. The probability that more than 6 of 20 randomly selected people are age 65 or older. According to the 2000 census, 12.4% of the population was age 65 or older. 36. The probability that less than 4 of 20 randomly selected people are age 65 or older. According to the 2000 census, 12.4% of the population was age 65 or older Chapter l Skills Practice

23 Skills Practice Skills Practice for Lesson.3 Name Date Charge It! Continuous Data and the Normal Probability Distribution Vocabulary Write the term from the box that best completes each statement. continuous data normal distribution normal curve Empirical Rule for Normal Distributions 1. A(n) is a curve that is bell-shaped and symmetric about the mean. 2. A(n) describes a continuous data set that can be modeled using a normal curve. 3. The states that approximately 68% of the area under the normal curve is within one standard deviation of the mean. 4. is data that has an infinite number of possible values. Problem Set Determine whether each type of data is continuous or discrete. 1. amount of rain that fell each day this year continuous 2. weight of puppies in the pet store 3. number of classrooms in schools across the state 4. number of vowels in the first names of your friends 5. pounds of cherries used to make pies Chapter l Skills Practice 1039

24 6. percent of passes the quarterback completed each game Label each number line so that the curve is a normal curve and follows the properties of the normal distribution. Include three standard deviations above and below the mean. 7. mean 5, standard deviation mean 20, standard deviation mean 4, standard deviation mean 10, standard deviation mean 72, standard deviation mean 50, standard deviation Chapter l Skills Practice

25 Name Date Mr. Fasse gave a test to his precalculus class. The mean score was 76 and the standard deviation was 6. The test scores follow a normal distribution. Answer each question about this test. 13. Approximately 68% of the students scored between what two numbers? ; About 68% of the students scored between 70 and 82 on the test. 14. Approximately 95% of the students scored between what two numbers? 15. Half of the students scored above what number? 16. Approximately 16% of the students scored above what number?. Approximately 2.5% of the students scored below what number? 18. Approximately 99.7% of the students scored between what two numbers? Chapter l Skills Practice 1041

26 The employees at a company drove an average of 15 miles each way to work with a standard deviation of 4.2 miles. The miles follow a normal distribution. Answer each question about the employees. 19. Approximately 68% of the employees drive between what two numbers of miles? ; About 68% of the employees drive between 10.8 and 19.2 miles. 20. Approximately 95% of the employees drive between what two numbers of miles? 21. Half of the employees drive less than how many miles? 22. Approximately 16% of the employees drive less than how many miles? 23. Approximately 2.5% of the employees drive more than how many miles? 24. Approximately 99.7% of the employees drive between what two numbers of miles? 1042 Chapter l Skills Practice

27 Skills Practice Skills Practice for Lesson.4 Name Date Recharge It! The Standard Normal Probability Distribution Vocabulary Define the term in your own words. 1. standard normal distribution Problem Set Draw a normal curve with each mean and standard deviation. 1. mean 60, standard deviation mean 60, standard deviation 5 Chapter l Skills Practice 1043

28 3. mean 100, standard deviation mean 100, standard deviation mean 10, standard deviation 2 6. mean 10, standard deviation Chapter l Skills Practice

29 Name Date Shade the area under the standard normal distribution curve that represents each percentage. Then, calculate each percentage. 7. The percentage of data above 0 standard deviations % of the data values are above 0 standard deviations. 8. The percentage of data between 0 and 1 standard deviations. 9. The percentage of data between 0 and 2 standard deviations. Chapter l Skills Practice 1045

30 10. The percentage of data between 1 and 3 standard deviations. 11. The percentage of data below 2 standard deviations. 12. The percentage of data above 1 standard deviation Chapter l Skills Practice

31 Name Date A light bulb has an average life of 1000 hours with a standard deviation of 40 hours. The standard normal distribution is shown. Determine the number of hours that is represented by each value. Explain represents hours because 960 hours is 1 standard deviation from the mean Chapter l Skills Practice 1047

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33 Skills Practice Skills Practice for Lesson.5 Name Date Catching Some Z s? Z-Scores and the Standard Normal Distribution Vocabulary Define the term in your own words. 1. z-score Problem Set A value on the standard normal curve is given. Describe the value on the normal curve that corresponds with the given value on the standard normal curve A value of 0 on the standard normal curve means the value is 0 standard deviations from the mean. Therefore, it is the mean Chapter l Skills Practice 1049

34 A data set has a mean of 8 and standard deviation of 0.4. Calculate the z-score for each data value. 7. a data value of 7 8. a data value of 8.15 z a data value of a data value of a data value of a data value of 7.8 Determine the area under the standard normal curve below each z-score using the z-score table. Then, label the z-score on the number line and shade the area below the z-score. 13. z z 1.25 area z z Chapter l Skills Practice

35 Name Date. z z 3.15 Determine the area under the standard normal curve below each z-score using a graphing calculator. 19. z z 2.79 area z z z z 1.23 Starting salaries for teachers in a given district have a mean of $38,000 with a standard deviation of $2500. Use this information to answer each question. 25. What percentage of the teachers in this district earn less than $30,000? 30,000 38,000 z Look up 3.2 in the z-score table. The area below this score is Therefore, 0.07% of the teachers in this district earn less than $30, What percentage of the teachers in this district earn less than $45,000? Chapter l Skills Practice 1051

36 27. What percentage of the teachers in this district earn less than $41,000? 28. What is the probability that a randomly selected teacher in this district earns less than $37,000? 29. What is the probability that a randomly selected teacher in this district earns less than $37,500? 30. What is the probability that a randomly selected teacher in this district earns less than $42,500? 1052 Chapter l Skills Practice

37 Skills Practice Skills Practice for Lesson.6 Name Date Above and In-Between Probabilities Above and Between Z-Scores Problem Set Determine the area under the standard normal curve above each z-score using the z-score table. Then, label the z-score on the number line and shade the area above the z-score. 1. z z z z z z 3.36 Chapter l Skills Practice 1053

38 Determine the area under the standard normal curve above each z-score using a graphing calculator. 7. z z 2.12 area z z z z 2.37 Determine the area under the standard normal curve between each pair of z-scores using the z-score table. Then, label the z-scores on the number line and shade the area between the z-scores. 13. z 2.0 and z 3.0 area z 0.46 and z Chapter l Skills Practice

39 Name Date 15. z 0.11 and z z 2.74 and z z 0.84 and z z 1.99 and z 1.56 Chapter l Skills Practice 1055

40 Determine the area under the standard normal curve between each pair of z-scores using a graphing calculator. 19. z 1.58 and z z 0.91 and z 0.35 area z 0.28 and z z 0.77 and z z 2.43 and z z 2.08 and z 1.62 The mean number of customers at a clothing store on a randomly selected day is 260 with a standard deviation of 110 customers. Calculate the probability that on a randomly selected day the store will have the indicated number of customers. 25. more than 250 customers z Using a graphing calculator, the area above z is The probability that there are more than 250 customers on a randomly selected day is more than 420 customers 27. less than 225 customers 1056 Chapter l Skills Practice

41 Name Date 28. less than 82 customers 29. between 310 and 350 customers 30. between 75 and 205 customers Chapter l Skills Practice 1057

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43 Skills Practice Skills Practice for Lesson.7 Name Date The Old, The News, and Making the Grade Applications of the Normal Distribution Problem Set The mean number of days of sunshine per year in a city is 258 days with a standard deviation of 26 days. Use this information to answer each question. 1. What percentage of years has more than 280 days of sunshine? z Using a graphing calculator, the area under the standard normal curve below z is Therefore, the percentage of years that has more than 280 days of sunshine is about or 19.87%. 2. Determine the probability that a randomly selected year has less than 250 days of sunshine. 3. Determine the probability that a randomly selected year has more than 232 days of sunshine. 4. What percentage of years has less than 271 days of sunshine? Chapter l Skills Practice 1059

44 5. What percentage of years has between 260 and 290 days of sunshine? 6. Determine the probability that a randomly selected year has between 240 and 265 days of sunshine. The mean time for a bobsledder to complete a run in a competition is 48 seconds with a standard deviation of 3 seconds. Use this information to answer each question. 7. Determine the probability that the bobsledder will complete a run in less than 45 seconds. z Using a graphing calculator, the area under the standard normal curve below z 1 is Therefore, the probability that the bobsledder will complete a run in less than 45 seconds is or 15.87%. 8. What percentage of runs will be completed in less than 50 seconds? 1060 Chapter l Skills Practice

45 Name Date 9. What percentage of runs will be completed in more than 54.5 seconds? 10. Determine the probability that the bobsledder will complete a run in more than 40 seconds. 11. Determine the probability that the bobsledder will complete a run in between 42 and 47 seconds. Chapter l Skills Practice 1061

46 12. What percentage of runs will be completed in between 46.2 and 49.8 seconds? The mean number of cell phone minutes Marlene uses each month is 420 minutes with a standard deviation of 125 minutes. Use this information to answer each question. 13. Determine the probability that Marlene will use less than 450 minutes in a month. z Using a graphing calculator, the area under the standard normal curve below z 0.24 is Therefore, the probability that Marlene will use less than 450 minutes in a month is or 59.48%. 14. Determine the probability that Marlene will use less than 330 minutes in a month. 15. What percentage of months will Marlene use more than 200 minutes per month? 1062 Chapter l Skills Practice

47 Name Date 16. What percentage of months will Marlene use more than 500 minutes per month?. What percentage of months will Marlene use between 400 and 600 minutes per month? 18. Determine the probability that Marlene will use between 150 and 375 minutes in a month. Chapter l Skills Practice 1063

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