objective green yellow red

Math 20-2: Unit 4 Statistical Reasoning Practice Booklet

Objective Green Yellow Red

4.0a Determine, interpret and compare the measures of central tendency for sets of data,

including: mean, median, mode, outliers, range.

4.0b Organize data into line plots, histograms & frequency polygons and interpret the data.

4.1 Determine, using technology, the standard deviation of a set of data.

4.2 Solve a contextual problem that involves the interpretation of standard deviation.

4.3 Explain, using examples representing multiple perspectives, the application of

standard deviation for making decisions in situations such as warranties, insurance or

opinion polls.

4.4 Demonstrate an understanding of normal distribution and explain the properties of a

normal curve, including: the mean, median, mode, standard deviation, z-scores,

symmetry and area under the curve.

4.5 Determine if a set of data approximates a normal distribution, and explain the

reasoning.

4.6 Determine, with or without technology, and explain the z-score for a given value in a

normally distributed set of data.

4.7 Compare the properties of two or more normally distributed sets of data.

4.8 Solve a contextual problem that involves normal distribution.

4.9 ** Students are NOT expected to calculate confidence intervals or margins of error. The

emphasis of this outcome is intended to be on interpretation rather than statistical calculations. 4.9a Explain using examples, the significance of a confidence interval, margin of error or

confidence level.

4.9b Interpret statistical data using confidence intervals, confidence levels and margin of

error.

4.9c Explain, using examples, how confidence levels, margin of error and confidence

intervals may vary depending on the size of the random sample.

4.9d Make inferences about a population from sample data, using given confidence

intervals, and explain the reasoning.

4.9e Provide examples from print or electronic media in which confidence intervals and

confidence levels are used to support a particular position.

4.9f Interpret and explain confidence intervals and margin of error, using examples found

in print or electronic media.

4.9g Support a position by analyzing statistical data presented in the media.


4a) Statistics Introduction

4.0 a) Determine, interpret and compare the measures of central tendency for sets of data, including:

mean, median, mode, outliers, range.

b) Organize data into line plots, histograms & frequency polygons and interpret the data.

Use this information to answer questions 1 & 2:

54 51 56 55 54 58 54 59 53 57 55 53 52 66 57

1. Ari obtained the heights of the boys in his brother‟s junior Tae Kwan Do class (list above).

Describe how you can best organize the data to determine the mean, median, mode, range, and any outliers.

2. Match each term with the appropriate value for the data in the list above question 1.

a) _______ Mean i) 54

ii) 3

b) _______ Median iii) 55.6

iv) 59

c) _______ Mode v) 55

vi) 15

d) _______ Outlier vii) 66

e) _______ Range

3. Determine the mean, median, mode, and range for the following list of data. Use the first of the 3 ways to calculate the mean. Show your work & round the mean to 1 decimal place.

24 31 28 43 52 19 27 44 33 22 27

Arrange least to greatest:

Mean = ____________ Median = ____________ Mode = ____________ Range = ____________

4. Which measure of central tendency (mean, median, mode) would be most useful for analyzing data in each of the following situations? a) the size of jeans to be stocked in a department store ____________

b) the masses of individual granola bars in a shipment ____________

c) the numbers of hours of daily sunlight during the month of February in Whitehorse ____________


Use this information to answer question #5.

Alaina records the number of text messages she receives each day for a month on a line plot.

5. a) On how many days did Alaina receive 32 texts? ________________ b) What is the mode of Alaina‟s data set? ________________

c) What is the range of the data set? ________________

d) Identify any outliers in the data. ________________

e) Determine the median of the data. ________________

6. Sara‟s teacher gave her class 10 quizzes, each worth 20 marks. Sara‟s marks on the quizzes are given below.

16 15 18 16 17 4 18 19 18 15

a) Determine the mean, median and mode of her marks.

Mean = ____________ Median = ____________ Mode = ____________

b) Which mark might be considered to be an outlier? ________________

c) Discard the outlier and then determine the mean, median, and mode.

Mean = ____________ Median = ____________ Mode = ____________

d) Which measure of central tendency is most affected by an outlier? ________________

e) Which measure of central tendency is least affected by an outlier? ________________

7. Joe and Josephine travel together by car to work. Joe says that the mean time to get to work is 23.0 min, while Josephine says that it is 20.5 min. Suggest a reason for the discrepancy. Could both mean times be correct? Yes or No

8. Frank and Frances work out at their local gym. The mean of their workout times is the same: 48 min. However, the range of Frank‟s workout times is 7 min, while the range of Frances‟s workout times is 16 min. Explain how this is possible.


9. Harrison recorded the length of time, rounded to the nearest 10 min, that he spent playing video games each day for a month.

Time (min) 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Frequency 1 0 0 4 3 5 4 5 8 7 9 6 4 0 0 2

a) Construct a line plot of the data.

b) Comment on the distribution of the data.

c) Identify any outliers in the data. ______________________________________________________

10. Calculate the missing value when given the mean and all data values but one in a list of data. Show your work. a) If the mean of the data set {10, 4, 7, 12, 9, 4, _x_, 6 } is seven, find the missing value „x‟.

Record your answer in the numerical response box. Round to the nearest tenth if necessary.

b) If the mean of the data set {20, 10, 14, 15, 9, _x_, 9, 8} is twelve, find the missing value „x‟. Record your answer in the numerical response box. Round to the nearest tenth if necessary.


11. Calculate the mean of the following using the equation: .

a) n = 100, p = 0.6 b) p = 0.65, n = 880 c) p = 0.05, n = 2000

12. The Gallup Poll once asked a random sample of 1540 adults, “Do you happen to jog?” Suppose that in fact 15% of all American adults jog. Find the mean of the proportion of the sample who jog.

4b) Frequency Tables & Histograms 4.0 b) Organize data into line plots, histograms & frequency polygons and interpret the data.

1. Jerry uses the internet to help him complete his homework. He recorded the time he spent online each day for one month. He grouped the data in a frequency table as shown below. a) On the first day of the month, he was online for 1.45 hours. In which interval did he record this time?

Interval: _________________________ hours

b) Use the grid provided to create a frequency polygon representing the data. Be sure to label & name the graph appropriately.

c) Describe how the data is distributed.

Internet Time (h)

Frequency

0.5 – 1.0 0

1.0 – 1.5 4

1.5 – 2.0 6

2.0 – 2.5 7

2.5 – 3.0 8

3.0 – 3.5 1

3.5 – 4.0 1

4.0 – 4.5 1

4.5 – 5.0 0

5.0 – 5.5 2

5.5 – 6.0 1


2. Tim is an apprentice at a bakery. The times he spends after school at the bakery, in hours, over one month are shown. 2.5 3.0 3.5 4.0 5.0 5.0 1.5 2.0 3.0 3.0 5.0 6.0 3.0 2.0 7.0 1.0 2.5 2.5 2.5 4.0 4.0 3.0 3.0 3.0 2.0 3.5 7.0 2.5 2.5 8.0

a) Suggest an appropriate interval width to represent how the data is distributed.

b) Complete the frequency distribution table. c) Use the grid provided to construct a histogram of the data.

Be sure to label & name the graph appropriately. d) Describe how the data is distributed.

3. The mathematics test scores for Tony‟s class were grouped and displayed using the frequency polygon to the right. a) What interval width was used when

grouping the data? ____________________

b) Tony says the most frequently occurring test score was 75%. Is she correct? Explain.

Time (h) Frequency


4. Serena works after school at the family convenience store. The hours she worked some days after school and on weekends in February are shown. 2.5 2.0 3.0 2.5 5.0 7.0 3.0 4.0 3.0 4.0 4.5 6.0

2.0 2.5 1.0 3.5 0.5 3.5 2.5 4.0 4.0 3.0 8.0 7.5

a) Suggest an appropriate interval width to represent how the data is distributed.

b) Complete the frequency distribution table. c) Use the grid provided to construct a frequency polygon

showing the distribution of the time Serena worked. Be sure to label & name the graph appropriately.

d) Describe how the data is distributed.

5. What do histograms and frequency polygons have in common? A. They both show percents. C. They both connect interval midpoints. B. They both have bars. D. They both show frequency data.

4c) Standard Deviation

4.0a Determine, interpret and compare the measures of central tendency for sets of data, including:

mean, median, mode, outliers, range.

4.1 Determine, using technology, the standard deviation of a set of data.

4.2 Solve a contextual problem that involves the interpretation of standard deviation.

4.3 Explain, using examples representing multiple perspectives, the application of standard deviation for

making decisions in situations such as warranties, insurance or opinion polls.

1. a) A survey was taken to find out how many people exercise twice or more a week. 2300 adults were surveyed. 34% of the people said yes. Find the mean and standard deviation of the proportion of the sample who exercise twice or more a week. Round to the nearest tenth where necessary.

Time (h) Frequency


b) According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A random sample of 300 children is selected for a study of learning in early childhood. What is the mean number of children in the sample who come from poverty-level households? What is the standard deviation of this number? Round to the nearest tenth where necessary.

2. Out of 320 people surveyed, 70% said „yes‟ they brush their teeth before bed. Determine the mean number of people from this group that brush their teeth before bed and the standard deviation of this group. Round to the nearest tenth where necessary.

3. The maximum daily temperatures for Sylvan Lake over a 7 day period are shown.

7.2, 4.8, 4.8, 2.0, 4.1, 12.7, 16.8. To the nearest tenth, calculate the… Mean = ______________

Median = ______________

Mode = ______________

Range = ______________

Standard Deviation = _________

4. Jarome Iginla‟s points for the Calgary Flames from 1997 to 2010 are shown in the table. a) Calculate the mean & standard deviation of the points Jarome Iginla earned from 1997 to 2010,

each to one decimal place. mean = ________________ standard deviation = ________________

b) Explain what the values in „a‟ mean.

c) Determine and explain the effect on the mean & standard deviation when the two lowest points are removed.

mean = ________________ standard deviation = ________________

Season Points

1997 – 1998 32

1998 – 1999 51

1999 – 2000 63

2000 – 2001 71

2001 – 2002 96

2002 – 2003 67

2003 – 2004 73

2004 – 2005 67

2005 – 2006 94

2006 – 2007 98

2007 – 2008 89

2008 – 2009 69

2009 – 2010 86


5. The “Postage Stamp”, the 8th hole at Royal Troon Golf Club in Scotland, is one of the most difficult short par threes in champion golf. During a recent tournament, the scores at that hole in the first round are shown. Calculate the mean & standard deviation, to the nearest tenth, of the number of strokes taken.

Mean = _______________ Standard = _______________ Deviation

6. Cricket, a game which is popular in Australia, the Indian sub-continent, South Africa, and the West Indies, originated in England. The data shows the number of runs scored by two players, Billy and Mark, in various innings. a) On average, who is the better player? Why? Explain.

b) Which player is more consistent? Why? Explain.

7. The table shows the number of shots per game by a defensive hockey player during the course of one season. . To the nearest tenth, calculate the… Mean = ___________________

Median = ___________________

Mode = ___________________

Standard Deviation = _____________

# of strokes Frequency

2 3

3 58

4 47

5 8

6 3

7 1

Billy Mark

37 56

1 20

24 12

33 21

106 77

68 34

82 49

31 38

5 14

45 45

# Shots # of Games

0 5

1 11

2 5

3 6

4 3

5 2

6 1


8. The means and standard deviations of math scores on a test of two different classes are shown in the table. Which class performed better on the test? Explain.

9. The ages of the grandparents of thirty two of Elaine‟s classmates were collected. 65 70 60 74 71 75 56 68 85 72 82 83 62 72 64 81 71 90 71 78 73 65 74 69 71 74 61 75 70 76 80 69 i) Calculate the mean & standard deviation, to the nearest tenth.

mean = ________________ standard deviation = ________________

ii) Calculate the value of the following, to the nearest tenth.

a) b) c) d)

iii) Calculate the percent of data μ ± 1σ _____________ to the nearest percent.

iv) Calculate the percent of data μ ± 2σ _____________

to the nearest percent.

Use the following information to answer the next question.

Katie played 15 rounds of golf at Fox Hollow GC and 18 rounds of golf at Shaganappi GC. At Fox Hollow, her mean score was 85.2, with a standard deviation of 4.4, and at Shaganappi, her mean score was 81.8, with a standard deviation of 2.7.

10. The standard deviation of Katie‟s scores for the two golf courses, indicates that her… a) Average score was better at Fox Hollow b) Average score was better at Shaganappi c) Scores were more consistent at Fox Hollow d) Scores were more consistent at Shaganappi

Class Mean Standard Deviation

A 69.5 2.7

B 70.2 7.5


4d) Normal Distribution: The Bell Curve & Z-Scores

4.4 Demonstrate an understanding of normal distribution and explain the properties of a normal curve,

including: the mean, median, mode, standard deviation, z-scores, symmetry and area under the curve.

4.5 Determine if a data set approximates a normal distribution, and explain the reasoning.

4.6 Determine, with or without technology, and explain the z-score for a given value in a normally distributed

data set.

4.7 Compare the properties of two or more normally distributed sets of data.

4.8 Solve a contextual problem that involves normal distribution.

1. State 5 properties of a normal distribution curve.

2. State the mean & standard deviation of the standard normal distribution.

Mean = ___________ Standard Deviation = ___________

3. What are z-scores and why do we calculate them? Explain their significance.

4. Calculate, to the nearest hundredth, the z-scores for the following:

a) μ = 200 σ = 25.4 x = 250 c) μ = 18 σ = 2.2 x = 17

b) μ = 260 σ = 12.5 x = 289 d) μ = 3.2 σ = 0.3 x = 2.7

5. The goals scored by a major league hockey player over 12 seasons are shown.

11, 18, 23, 27, 21, 30, 28, 24, 17, 21, 19, 24

a) Calculate the mean and standard deviation, each to the nearest hundredth. Mean = ___________ Standard Deviation = ___________


b) Assuming the data is normally distributed, calculate the z-scores, to the nearest hundredth, for the highest and lowest number of goals.

6. At the Growers Apple Festival, a panel of ten judges award points, on a scale of 1 to 10, in order to determine the most appealing apples. One particular apple had an overall score of 89 with a z-score of 2.35. If the data was normally distributed with a standard deviation of 8.5, determine the overall mean of the data, to the nearest whole number. Record your answer in the numerical response box starting on the left.

7. Pat‟s unit test marks are shown below, together with the class mean and standard deviation for each unit test. By calculating z-scores, determine, relative to the rest of the class, in which unit test Pat performed:

a) Best: ____________________________

b) Worst: ____________________________

8. On a nursing proficiency exam at a Canadian college, the mean score was 63 and the standard deviation was 10. If Nicole‟s z-score was 1.7, then what was her actual exam mark to the nearest whole number? Record your answer in the numerical response box starting on the left.

9. At a local fruit stand, they sell an average of 575 kg of cherries per week. If they sold 478 kg last week, which was 1.73 standard deviations below the mean (z-score), and if the data is normally distributed, then determine the standard deviation to the nearest tenth of a kg. Record your answer in the numerical response box starting on the left.

Subject Pat‟s Mark

Mean Mark

Standard Deviation

Z-Score

Radicals 79 70 12

Trigonometry 78 68 13

Quadratics 71 61 14

Statistics 76 65 13


4e) Calculating Probability & Area Under the Normal Distribution Curve

1. Find the probability (area under the standard normal curve) for each z-score interval. For each, sketch the graph & round the area to 4 decimal places and then round the percent from the area to 2 decimal places. a) z < –1.6 b) z > –1.6 c) z > 1.6 d) z < 1.97 e) –1.6 < z < 1.6 f) 0.85 < z < 1.24 g) –2.5 < z < 1.5

2. Calculate the z-scores, rounded to the nearest hundredth, that are required for each situation. Write the calculator process, sketch the graph and shade the section indicated for each. a) 15% of the data is to the right of the z-score

Area = ___________________ Z-Score = ____________

b) 15% of the data is to the left of the z-score Area = ___________________ Z-Score = ____________

c) 57% of the data is above the z-score

Area = ___________________ Z-Score = ____________


3. Find the value of „a‟. Write the calculator process and sketch each graph shading the indicated sections.

a) P(z < a) = 0.1379 b) P(a < z < 0) = 0.4306

4. The area, to the nearest tenth of a percent, under the standard normal distribution curve which lies within 1.5 standard deviations of the mean is ______________. Record your answer in the numerical response box starting on the left.

5. The shaded area in the diagram represents 23.97% of the area under the standard normal distribution curve.

The value of z1 is

A. –0.92 B. –0.71 C. –0.64 D. –0.52

4f) Applications of the Normal Distribution

1. The results of a provincial Grade Nine achievement test were normally distributed with a mean of 68 and a standard deviation of 12. If 8500 students wrote the test… a) determine the percentage of students,

to the nearest tenth of a percent, who scored a mark of 50 or above, sketch the graph & shade the appropriate region.

b) determine the number of students who scored a mark of 50 or more. _____________________

c) sketch each graph (shading the appropriate regions) & determine the probability that a student selected at random had a mark:

i. Less than 30 ii) between 50 and 60


2. The “Long Life” battery company is planning to add another 10 500 batteries to their yearly production of batteries. The mean life of “Long Life” batteries is estimated to be 50 hours with a standard deviation of 6 hours. If the data is normally distributed, then how many of the new batteries to be produced can be expected to last less than 31 hours? Sketch the graph & shade the appropriate region.

z = __________ P (z < __________ ) = A ( __________ ) = ______ Batteries

3. The heights of 800 officers from a police force are normally distributed with a mean of 175 cm and a standard deviation of 8 cm. a) How many of the officers are within one standard deviation of the mean height? ______________

b) How many officers are between 167 and 173 cm? ______________ Z-Score for 167 = __________ Z-Score for 173 = __________ Probability between 167 & 173 = __________________ (rounded to 4 decimal places)

c) What percentage of the officers, to the nearest hundredth, is between 165 cm and 180 cm? ________ Z-Score for 165 = __________ Z-Score for 180 = __________ Probability between 165 & 180 = __________________ (rounded to 4 decimal places)

4. Data collected of cars passing on a road revealed that the average speed was 90 km/h with a standard deviation of 5 km/h and data which is normally distributed. A policeman sets up a photo radar on a road with a speed limit of 80 km/h. The policeman sets the camera so that only those exceeding the limit by 10% are photographed & ticketed. a) What is the lowest speed, in km/h, for which you could be ticketed? ____________

b) If 60 cars pass the photo radar, how many drivers can the police expect to ticket? __________ i) z-score for lowest speed to be ticketed = _________ ii) the probability (rounded to 4 decimal places) for drivers over the z-score from part „i‟ = __________________


5. The results of a provincial achievement test are normally distributed and are represented in the diagram below. The data under the curve represents all of the students who wrote the test. The values 452 and 2500 represent the number of students in the shaded regions shown. a) How many students wrote the test?

b) To the nearest hundredth, what is the value of z1?

c) What percentage, to the nearest hundredth, does the area shaded in the diagram represent?

6. The data below the curve is normally distributed and represents the birth weights of a large number of babies.

To the nearest hundredth, what is the value of z1?

7. After reviewing previous loan records, the credit manager of a bank determines that the data follows a normal distribution. The debts have a mean of $20 000 and the probability that the loss could be greater than $25 000 or less than $15 000 is 0.418. Determine the standard deviation of the data to the nearest hundred dollars. Sketch the graph & shade the appropriate regions. Z-Score 1 for 15 000 = _____________ Z-Score 2 for 25 000 = _____________ Standard Deviation = ____________

8. A company packages rice into 10 kg bags. The machine that fills the bags can be calibrated to fill any

specified mean with a standard deviation of 0.09 kg. Any bags that weigh less than 10 kg cannot be sold and must be refilled. To what mean value, to the nearest hundredth of a kilogram, should the machine be set for if the company does NOT want to refill more than 1.5% of the bags. Percentage to Probability = ______________ Z-Score for the probability = _____________ Mean = _______________


9. A star offensive hockey player averaged 611 shots per season with a standard deviation of 57 shots. The number of shots per season is normally distributed. If the player played for 16 seasons, then the number of seasons the player had at least 675 shots is

A. 1 Z-Score for 675 = _________________ B. 2 (rounded to 2 decimal places) C. 3 Probability/ Area = _____________ D. 4 (rounded to 4 decimal places)

Unit 4 Answer Key Unit 4 Answer Key 4a

1. 2. a) iii b) v c) i d) vii e) vi 3. mean = 38.818… median = 28, mode = 27, range = 33 4. a) mode b) mean c) median 5. a) 2 b) 27 c) 14 d) 36 e) 27 6. a) mean = 15.6 median = 16.5 mode = 18 b) outlier = 4 c) mean = 16.888… median = 17 mode = 18 6. d) mean e) mode 7. Answers will vary, ex: Perhaps, for a few days, they had to drive through construction which took a lot longer. Joe may have included those times in his calculations where Josephine may not have included them which would account for the difference. Therefore, both means are correct. 8. Answers will vary, ex: Frank‟s workout times are all about the same length of time. Frances sometimes has long workouts and sometimes has shorter workouts. 9. b) most of the data is clustered from 110 to 140 min. Nearly all of the data is between 60 min and 150 min. c) Outliers are: 30 min and 180 min. 10. a) 4 b) 11 11. a) 60 b) 572 c) 100 12. 231


4b 1. a) Interval: 1.0 – 1.5 hours b) frequency polygon graph: c) The data is distributed with most grouped between 1 to 3 hours. This means that Jerry spends an average of 1 to 3 hours per day using the internet to help with his homework. 2. a) 7 intervals of 1 hour b) frequency table: c) histogram: d) The data is distributed with most grouped between 1 to 3 hours. This means that for most of the month Tim spends 2/3 of his shifts working between of 1 to 4 hours at the bakery and about 1/3 of his shifts are longer than 4 hours. 3. a) 7 intervals of 1 hour b) frequency table: c) histogram: 3. d) Serena works an average of 2 to 5 hours per shift in February at her father‟s convenience store and very few shifts over 5 hours. 4. a) Intervals of 10% b) NO he is not correct because the data was initially grouped, so he can only determine from the graph that most of the data lies between 71 – 80. This means that most of Tony‟s class scored between 71% - 80% . 5. D 4c 1. a) mean = 782 standard deviation = 22.7 b) mean = 66 standard deviation = 7.2. 2. 224, = 8.2

3. Mean = 7.5 C median = 4.8 C mode = 4.8 C range = 14.8 C (16.8 – 2.0) standard deviation = 4.9 C 4. a) mean = 73.6 standard deviation = 18.3 b) This means that Jarome scored an average of 73.6 goals per season with an approximate 18.3 point spread between the data. c) without the 2 lowest scores the standard deviation is lower which means Jarome‟s point production was more consistent which also makes his mean point production higher. 5. Mean = 3.6 standard deviation = 0.8 6. a) Billy is the better player because he has the higher average (mean). b) Mark is more consistent because he has a lower standard deviation. 7. Mean = 2.0 median = 2 mode = 1 standard deviation = 1.6 8. Class A performed better because it has a lower standard deviation which indicates that the test scores were more consistent and closer to the mean. 9. i) mean = 72.1 years standard deviation = 7.4 years ii) a) 64.7 b) 79.5 c) 57.3 d) 86.9 iii) 21 / 32 = 66% iv) 30 / 32 = 94%

Time (h) Frequency

1 – 2 2

2 – 3 9

3 – 4 9

4 – 5 3

5 – 6 3

6 – 7 1

7 – 8 3

Time (h) Frequency

1 – 2 2

2 – 3 6

3 – 4 6

4 – 5 5

5 – 6 1

6 – 7 1

7 – 8 3


4d 1. i) the total area under the curve is equal to 1; ii) the curve extends infinitely to the left and right; iii) the curve is symmetrical about the mean, where half of the data (50%) is below the mean and half of the data (50%) is above the mean; iv) all the data is represented by the area under the curve; and v) the mean, median and mode are the same value. 2. Mean = 0 and Standard Deviation = 1 3. i) Z-scores are standardized values calculated from normally distributed data that indicate the number of standard deviations that a data value is above or below the mean, where comparatively, the mean is 0 and the standard deviation is 1; ii) A positive z-score indicates that a data point is above the mean and a negative z-score indicates that a data point is below the mean; iii) Z-scores are used to compare different sets of data that do not have the same mean and / or standard deviation. 4. a) z = 1.97, b) z=2.32, c) z= – 0.45, d) z= – 1.67 5. a) Mean = 21.92 and Standard Deviation = 5.06 b) z-score for the lowest (11) = – 2.16 And, z-score for the hightest (30) = 1.60 6. Mean = 69 7. a) best= Statistics b) worst = Trigonometry 8. Actual Mark = 80% 9. Standard deviation = 56.1 kg 4e) 1. a) 0.0548, 5.48% b) 0.9452, 94.52% c) 0.0548, 5.48% d) 0.9756, 97.56% e) 0.8904, 89.04% f) 0.0902, 9.02% g) 0.9270, 92.70% 2. a) area = 0.85, z = 1.04 b) area = 0.15, z = – 1.04 c) area = 0.43, z = – 0.18 3. a) z = – 1.09 b) z = – 1.48 4. 86.6% 5. D 4f) 1. a) 93.3% b) 7932 students c) i) 0.0008 ii) 0.1846 2. 8 Batteries Z-score is – 3.17

P (z < – 3.17 ) = A (– 3.17 ) 3. a) z-scores = – 1 and 1, (800 x probability 0.6826) = 546 Officers b)

z-scores = – 1 and – 0.25 , (800 x probability 0.2426) = 194 Officers c) z-scores = – 1.25 and 0.63, probability = 0.6301 = 63.01% of the officers 4. a) 88 km/h (80x1.10) b) i) – 0.40 ii) 0.6554 = 39 drivers

ticketed (probability x 60 drivers) 5. a) 5000 students b) z1 = – 1.34 c) 59.04% = (452/5000 =

0.0904 + 0.5 = probability) 6. z1 = 1.84 7. z1 = – 0.81 and z2 = 0.81, standard deviation = $ 6 200.

8. probability = 0.0150 z1 = – 2.17, mean = 10.20 kg 9. B

objective green yellow red

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