Spring Semester Review AMDM - Tanksley Planet



NORMAL DISTRIBUTIONS

Know and apply the characteristics of the normal distribution (Notes at bottom).

|A set of data that is normally distributed has a mean of 35.6 and standard |The length of a certain species of fish was found to be normally distributed. |

|deviation of 2.5. Which of the following is between 1 and 2 standard |The mean length is 79 cm with a standard deviation of 11 cm. In a school of |

|deviations of the mean? |490 of these fish, how many would be longer than 101 cm? |

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|[A] 41.2 [B] 29 [C] 34.1 [D] 38.3 |[A] 12 [B] 66 [C] 167 [D] 478 |

| |[pic] |

|[pic] |The heights of a certain group of adult parrots was found to be normally |

| |distributed. The mean height is 35 cm with a standard deviation of 7 cm. In a |

|The length of a certain species of fish was found to be normally distributed. |group of 1200 of these birds, how many would be more than 28 cm tall? |

|The mean length is 84 cm with a standard deviation of 15 cm. In a school of |[pic] |

|450 of these fish, how many would be longer than 99 cm? | |

| |The height of a certain group of adult parrots was found to be normally |

|[A] 61 [B] 153 [C] 72 [D] 439 |distributed. The mean height is 35 cm with a standard deviation of 8 cm. In a |

| |group of 1000 of these birds, how many would be more than 19 cm tall? |

|[pic] | |

| |[pic] |

|The lengths of a certain species of fish were found to be normally |The heights of a certain group of adult parrots was found to be normally |

|distributed. The mean length is 78 cm with a standard deviation of 14 cm. In a|distributed. The mean height is 34 cm with a standard deviation of 8 cm. In a |

|school of 370 of these fish, how many would be longer than 92 cm? |group of 400 of these birds, how many would be more than 18 cm tall? |

| |[pic] |

|[A] 126 [B] 50 [C] 59 [D] 361 | |

|[pic] | |

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1. The heights of 1000 students at a local school were recorded and found to be approximated by the normal curve below. Which answer could represent the mean and standard deviation for these data?

[pic]

[A] 63, 8 [B] 67, 5 [C] 51, 4 [D] 63, 4

2. Compare the quantity in Column A with the quantity in Column B.

|Column A |Column B |

|Mean is 15, standard deviation |Mean is 35, standard deviation |

|is 4.3 3 standard deviations |is 2.9; 2 standard deviations |

|above the mean. |below the mean. |

[A] The quantity in Column A is greater.

[B] The quantity in Column B is greater.

[C] The two quantities are equal.

[D] The relationship cannot be determined on the basis of the information supplied.

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. (REMEMBER Z-score: [pic])

3. How many people in a group of 60 will have an IQ less than 92 if their IQs are normally

distributed with a mean of 100 and a standard deviation of 15?

A) 18 B) 29 C) 30 D) 42

4. Find the critical value z α/2 that corresponds to a 96% confidence level.

A) 1.75 B) 2.05 C) 2.33 D) 2.575

5. Given a normally-distributed data set whose mean is 40 and whose standard deviation is 8¨ what value of x would have a z-score of -1.25?

A) -10 B) 10 C) 30 D) 50

Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. [pic]

6. College students' annual earnings: 99% confidence; n = 68, x = $3068, σ = $818

A) $255 B) $194 C) $958 D) $231

7. Weights of eggs: 95% confidence; n = 45, x = 1.50 oz, σ = 0.20 oz

A) 0.01 oz B) 0.44 oz C) 0.06 oz D) 0.05 oz

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (μ, p, σ) for the indicated parameter.

8. A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.

A) H0: μ = 14 B) H0: μ > 14

H1: μ < 14 H1: μ ≤ 14

C) H0: μ = 14 D) H0: μ < 14

H1: μ > 14 H1: μ ≥ 14

9. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 40°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.

A) H0: μ ≠ 40° C) H0: μ ≤ 40°

H1: μ = 40° H1: μ > 40°

B) H0: μ ≥ 40° D) H0: μ = 40°

H1: μ < 40° H1: μ ≠ 40°

10. A psychologist claims that more than 6.1 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness.

A) H0: p < 6.1% C) H0: p > 6.1%

H1: p ≥ 6.1% H1: p ≤ 6.1%

B) H0: p = 6.1% D) H0: p = 6.1%

H1: p < 6.1% H1: p > 6.1%

11. You are going to survey a random sample of the 300 passengers on a flight from San Francisco to Tokyo. Identify each sampling method described below.

A. Randomly select the 10th passenger, and survey every 10th passenger as people board the plane.

B. From the alphabetized boarding list, randomly choose 5 people flying first class and 25 of the other passengers.

C. Randomly generate 30 seat numbers and survey the passengers who sit there.

D. Randomly select a seat position (right window, center, aisle, etc. ) and survey all of the passengers sitting in those seats.

E. Choose approachable-looking people that are waiting to board the plane.

F. Survey every passenger on the plane.

19. The data below shows the number of homeruns hit by Mark McGwire during the 1986-2000 seasons. Create a histogram to represent this data. Use a bin size of three years, and write the height of each bar above it.

|Year |homeruns |

|1986 |3 |

|1987 |49 |

|1988 |32 |

|1989 |33 |

|1990 |39 |

|1991 |22 |

|1992 |22 |

|1993 |6 |

|1994 |3 |

|1995 |39 |

|1996 |52 |

|1997 |58 |

|1998 |70 |

|1999 |65 |

|2000 |32 |

20. Below is data for the performances of fourth grade boys and girls on an agility test. The test asks them to jump from side to side across a set of parallel lines, counting the number of lines they can clear in 30 seconds.

Boys: 22 17 18 29 22 22 24 23 17 21

Girls: 25 20 12 19 28 24 22 21 25 26 25 16 27 22

Create two box & whiskers plots. Use the same scale for each.

21. A history teacher asked her students how many hours of sleep they had the night before a test. The data below shows the number of hours the students slept and their score on the exam.

| | | |Hours Slept |Test Score |

| | | |8 |83 |

| | | |7 |86 |

|  | | |7 |74 |

| | | |8 |88 |

| | | |6 |76 |

| | | |5 |63 |

| | | |7 |90 |

| | | |4 |60 |

| | | |9 |89 |

| | | |7 |81 |

A) Finish the statement: “A student who slept a higher number of hours had…

B) Does this graph exhibit a linear or non-linear pattern? Explain.

C) Is the graph representing a positive or negative relationship? Explain.

D) Describe the relative strength of the association between the variables.

E) Does this imply a cause and effect relationship? Explain.

22. Using the data from #21, answer the following questions: (round all values to four decimal places)

A. Calculate a regression equation and record it here.

B. What is the r2 value?

C. Using this regression equation, predict the score of someone who slept 6.5 hours.

D. Using this regression equation, predict the number of hours slept by someone who scored a 70.

23. Given the data set below, find the following. (round to four decimal places)

23, 43, 35, 34, 31, 28, 27, 36, 41, 39, 27, 26, 33, 34, 28, 25, 35, 27

[pic]

n value

five-number summary

|0 |19 |

|1 |23 |

|2 |27 |

|3 |31 |

24. Given the table:

A. Give a recursive rule for the sequence. B. Give an explicit rule for the sequence.

25. Given the sequence: 1000, 500, 250, 125, …

A. Give a recursive rule for the sequence. B. Give an explicit rule for the sequence.

C. If [pic], what is [pic]?

|Bounce # |Height (in cm) |

|0 |175 |

|1 | |

|2 | |

|3 | |

|4 | |

|5 | |

26. Complete the given table for a ball with a rebound percentage of 60%.

A. Write a recursive rule for the data.

B. Write an explicit rule for the data.

C. What is the height after the fourth bounce of this ball if it is dropped from a height of 250 cm?

D. If this ball is dropped from a height of 300 cm, how many times does it bounce before it has a bounce height of less than 4 cm?

27. Complete the given table for John’s new job. He gets $60 for being a salesman and $35 for each item he sells.

|Item(s) |Income |

|0 |60 |

|1 | |

|2 | |

|3 | |

|4 | |

|5 | |

A. Write a recursive rule for this relationship.

B. Write an explicit rule for this relationship.

C. How much money will he have if he sells 65 items?

D. How many items does he have to sell to make his quota of $5000, in order to keep his job?

E. What does the domain represent in this problem situation?

F. What does the range represent in this problem situation?

28. A specific disease infects a certain percentage of a fixed population each day.

|Day number |# people infected |

|0 |1 |

|1 |1 |

|2 |2 |

|3 |2 |

|4 |3 |

|5 |3 |

|6 |4 |

|7 |5 |

A. Generate an exponential equation for this data.

(round all values to 4 decimal places)

B. What is the infection rate? (round to a whole percent)

C. Generate a logistic equation for this data.

(round all values to 4 decimal places)

D. Using the logistic equation, predict the total population.

E. On what day will the entire population be infected? (

29. The data in the following tables describes the length of daylight in the given cities. Use your calculator to complete the table below. Round all points to the nearest whole number.

|Date |Day Number |Port Hedland, Australia, 20°|

| | |S |

| | |HH:MM |Min. |

|Jan. 1 |1 |13:20 |800 |

|Feb. 1 |32 |13:00 |780 |

|March 1 |60 |12:30 |750 |

|Apr. 1 |91 |11:54 |714 |

|May 1 |121 |11:22 |682 |

|June 1 |152 |10:59 |659 |

|July 1 |182 |10:55 |655 |

|Aug. 1 |213 |11:12 |672 |

|Sept. 1 |244 |11:42 |702 |

|Oct. 1 |274 |12:16 |736 |

|Nov. 1 |305 |12:51 |771 |

|Dec. 1 |335 |13:16 |796 |

|Date |Day Number |Guadalajara, Mexico, 20° N |

| | |HH:MM |Min. |

|Jan. 1 |1 |10:54 |654 |

|Feb. 1 |32 |11:15 |675 |

|March 1 |60 |11:45 |705 |

|Apr. 1 |91 |12:21 |741 |

|May 1 |121 |12:54 |774 |

|June 1 |152 |13:18 |798 |

|July 1 |182 |13:22 |802 |

|Aug. 1 |213 |13:03 |783 |

|Sept. 1 |244 |12:32 |752 |

|Oct. 1 |274 |11:57 |717 |

|Nov. 1 |305 |11:22 |682 |

|Dec. 1 |335 |10:58 |658 |

Use the following window: x min = 0 x max = 500

y min = 600 y max = 900

|City |Regression Model (round to four |Maximum |Minimum |First Intersection |Second Intersection |

| |decimal places) | | | | |

|Port Hedland|Calculator form: |Ordered pair: |Ordered pair: | | |

| | | | | | |

| | |Month: |Month: | | |

| | | | | | |

| | |Length of day: |Length of day: | | |

Spring Semester Review AQR

30. Coen decides to take a job with a company that sells magazine subscriptions. He is paid $20 to start selling and then earns $1.50 for each subscription he sells. Make a table that shows the amount of money (M) Coen earns for selling N subscriptions.

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31. Write a recursive rule for the amount of money Coen can earn selling magazine subscriptions.

32. Write a closed-form rule for the nth term in the sequence describing the amount of money Coen can earn,

33. Coen is trying to earn enough money to buy a new MP3 player. He needs $225 to cover the cost and tax on the MP3 player. How many magazine subscriptions does Coen need to sell to buy his new MP3 player? Justify your answer. Which rule did you use to answer this question? Why did you choose that rule?

34. Your phone service allows you to add international long distance to your phone. The cost is a $5 flat fee each month and $.03 a minute for calls made. Write a recursive rule describing your monthly cost for international calls. Then write a closed-form rule for the n minutes of calls made in a month.

35. How are recursive rules different from function rules for modeling linear data? How are they the same? When are recursive rules more useful than closed-form rules? When are closed-form rules more useful?

36. Be able to enter data from a chart into the graphing calculator to determine a regressed equation and how good a fit the equation is with respect to the raw data.

37. Be able to recognize a logistics curve given either data or a graph.

38. Be able to distinguish between a logistics curve and an exponential curve.

Derrick is trying to save money for the down payment on a used car. His parents have said that, in an effort to help him put aside money, they will pay him 10% interest on the money his accumulates each month. At the moment, he has saved $200.

39. Suppose Derrick does not add any money to the savings. Write a recursive rule and a closed-form function rule that model the money Derrick will accumulate with only the addition of the interest his parents pay.

40. How long will it take Derrick to save at least $2000 for the down payment if the only additions to his savings account are his parents’ interest payments?

41. In an effort to speed up the time needed to save $2000, Derrick decides to take on some jobs in his community. Suppose he commits to adding $50 per month to his savings. Make a table showing the amount of money Derrick will have over several months.

[pic]

42. Make a scatterplot of the data you generated in the table and compare the scatterplot to the function rule you found in question 11. How does adding $50 per month to his saving change the way in which his money grows?

[pic]

43. Can you write a recursive routine to model this situation? Can you write a closed-form function rule to model this situation? Explain your response.

44. How long will it take Derrick to save $2000 for the down payment if he contributes $50 every month? Explain how you arrived at your answer.

45. Suppose Derrick changes the amount of money he adds to his savings each month to $100. How does this affect the time it takes to save $2000? How much does he have to add to the savings each month to have enough money for the down payment on his car in 6 months?

46. Given the function: [pic]

|x |y |[pic][pic] |Difference Equation |

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47. All difference equations of exponential functions are what kind of functions?

48. All common ratios of exponential functions are found by doing what?

49. Where is the common ratio found in the exponential function?

50. Find the equation of the cyclical function.

51. What is the period of the function?

52. What is the amplitude of the function?

53. What is the centerline or vertical displacement?

54. What is the horizontal change or phase shift?

[pic]

60. What kind of function might model the data in your scatterplot?

61. The general form for an exponential function is y = a(b)x, where a represents the initial or original condition and b represents the successive ratio, or base of the exponential function. Using data from your table, write a function rule to describe the temperature of the coffee (y) as a function of time (x).

62. What do the constants in the explicit function rule represent?

63. If you repeated this experiment in a room that was much cooler, what data would you expect? Why do you think so?

64. What would a scatterplot of the change in temperature versus the difference between the liquid’s temperature and the ambient temperature look like? Use the graphing calculator to make a scatterplot of the change in temperature versus the difference between the liquid’s temperature and the ambient temperature. Describe your viewing window and sketch your graph.

65. What kind of function appears to model your graph?

66. Use an appropriate regression routine to find a function rule to model your data. Record your function rule, rounding to three decimal places.

Recall that a proportional relationship between the independent and dependent variables satisfies 3 criteria:

1) the graph is linear and passes through the origin

2) the function rule is of the form y = kx

3) the ratio [pic] is constant for all corresponding values of x and y.

67. Is your function rule a proportional relationship? Defend your answer using all three criteria:

Graph: Function Rule: Table:

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73. Calculate the rate of change of the number of bacteria over time. Fill in the rate of change column in the table. Use the calculator to help you.

74. What doe “rate of change” mean in the context of this situation?

75. What do you think a scatterplot of the rate of change versus the number of bacteria at a given time would look like?

76. Use the calculator to make a scatterplot of the rate of change versus the number of bacteria at a given time. Describe your window.

77. What type of function might best model the relationship between the rate of change and the number of bacteria?

78. Use an appropriate regression model to determine a function rule to find the rate of change (y) for a given number of bacteria (x).

79. Is your function a proportional relationship? (see # 77)

83. Do the same things to the values for Philadelphia and Porto Alegre.

84. What are the similarities and differences between the graphs of Houston, Philadelphia and Porto Alegre?

85. How does the maximum length of daylight for Philadelphia compare to the maximum length of daylight for Houston and Porto Alegre?

86. Use your calculator to determine the intersection points of the regression models for Houston, Philadelphia and Porto Alegre. Record these ordered pairs in the summary Table.

87. When is there more daylight in Houston than in Philadelphia and Porto Alegre? When is there less daylight in Houston than in Philadelphia or Porto Alegre?

88. What is the difference in latitude between Houston and Philadelphia? How do the latitudes between Houston and Porto Alegre compare?

Graph each city from #88 in a different color or style.

89.

90.

91.

92.

93.

94. What are the domain and range of the function that models the sound wave?

95. If the sound that Mr. Licefi’s class measured lasted for 8 seconds and stayed the same pitch, what re the domain and range of the sound wave?

96. Compare the domain and the range for the function that models the sound wave and the domain and range for the sound wave itself. Explain the similarities and the differences.

97. Bill is working at a tv store. He gets 20 dollars a day and 10 dollars for every tv he sells. Write a recursive and closed formula for this situation.

98. A colony of ants started at 42 ants and is growing at a daily rate of 7.2%. How many ants would be present 10 days later?

99. A ball has a rebound percentage of 50% and a start height of 120 cm. What is the total vertical distance the ball has traveled when it gets to its peak on the 6th bounce?

100. What type of function would be the best fit for the following data?

L1 L2

20 18

17 15

15 13

13 14

11 15

9 20

101. The following table shows the length of days for Trenton, NJ.

  |Jan. 1 |Feb. 1 |Mar. 1 |Apr. 1 |May. 1 |Jun. 1 |Jul. 1 |Aug. 1 |Sept. 1 |Oct. 1 |Nov. 1 |Dec. 1 | |Day # |1 |32 |60 |91 |121 |152 |182 |213 |244 |274 |305 |335 | |Min |552 |600 |672 |750 |828 |882 |888 |846 |774 |696 |618 |564 | |What is the equation for the length of day for Trenton (sinusoidal regression)? Find the minimum point using this equation.

102. Tommy got $1,200 for graduation. He plans to invest this in a savings account that earns 3.2% compounded monthly. How long will it take for that investment to be worth $100,000?

N = ____ I% = ____ PV = __________ PMT = ____ FV = __________ P/Y = ____ C/Y = ____

103. Billy got $10,000 as a bonus and wants to invest it in the bank. He plans to invest this in a savings account that earns 4.5% compounded monthly. How much will it be worth in 20 years?

N = ____ I% = ____ PV = __________ PMT = ____ FV = __________ P/Y = ____ C/Y = ____

104. Ashley is going to invest $250 monthly in an annuity for 25 years at 6.8% compounded monthly. What will be the value of this investment at the end of that time?

N = ____ I% = ____ PV = __________ PMT = ____ FV = __________ P/Y = ____ C/Y = ____

105. Mary wants to have $50,000 in 25 years after investing in an account that earns 5.12% interest compounded quarterly. How much will she have to invest now to make this goal?

N = ____ I% = ____ PV = __________ PMT = ____ FV = __________ P/Y = ____ C/Y = ____

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NOTES

[pic]

55. Complete the table by computing the first differences and successive ratios. Use the calculator’s lists to help with the computation by entering the time into List 1 and temperature into List 2. Use List Operations to find successive differences and successive ratios.

56. Is this relationship linear or exponential? How do you know?

57. Use the information in the table to build a recursive rule for each successive temperature reading.

58. What do the constants in the recursive rule represent?

59. Use your graphing calculator to make a scatterplot of temperature versus time and record your results and describe your viewing window.

60.

68. Under certain conditions, E.coli can grow at a rate that doubles its population in 1 hour. Use the growth rate to fill in the Number of Bacterial column in the table.

69. Identify the independent and dependent variables in this situation.

70. Use your graphing calculator to make a scatterplot of the number of bacterial versus time. Describe your viewing window.

71. What type of function do you think would model the data shown in your scatterplot?

72. Use an appropriate regression model to determine a function rule to find the number of bacteria (y) for a given time (x).

Enter the data into the calculator.

80. Use your calculator to generate a sinusoidal regression mode. Record the equation (round values to the nearest hundredth) in the Summary Table.

81. Factor the value of “b” from the quantity (bx + c) and include that form of the equation in the Summary Table.

82. Use your calculator to determine the maximum and minimum values for the length of daylight by day in Houston. Record these ordered pairs in your Summary table. To which dates do these maximum and minimum values correspond?

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