APPRECIATION

First of all, I would like to thank to my Additional Mathematics teacher, En Syauqi bin Md Salleh as he gave me important guidance to finish this project.

I also take this chance to express my gratitude to my beloved parents for encouraging me through my ups and downs. I hope I can do better for this upcoming SPM so they can feel proud of having me in their life.

I would also like to thank to my friend, Noor Aliah Afifah binti Mohd Ishak for helping me to finish this project.

Also for people who were involved directly or indirectly towards making this project into a reality.

Thank you for all your kindness.

OBJECTIVES

We, students who are taking Additional Mathematics are ordered to carry out a project work while we are in form 5. This year, the Curriculum Development Division, Ministry of Education Project Work, we can give valuable experience and are able to:

Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real life problems.

Acquire effective mathematical communication through oral and writing, and to use the language of mathematics to express mathematical ideas correctly.

Realize that mathematics is an important and powerful tool in solving real life problems and hence develop positive attitude towards mathematics.

Introduction.In statistics, there are two types of probability distributions, binomial distribution and normal distribution. These probability distributions are used widely to solve problem in real life information about the measure. Every student taking Additional Mathematics is required to carry out a project work in Form 5. This year, the curriculum developmet Division Ministry of Education has prepared a task about the probability distribution.Upon completation of the Additional Mathematics project work, I gain valuable experiences and able to:

Apply mathematics to everyday situations and appreciate the importance and the beauty of mathematics in everday lives.

Improve problem-solving skills, thinking skills, reasoning and mathematical communication.

Develop positive attitude and personalities and intrinsic mathematical values such as accuracy, confidence and systematic reasoning.

Stimulate learning environment that enhances effective learning, inquiry-based and team-work.

Develop mathematical knowledge in a way which increases students` interest and confidence.

A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times. The first variable in the binomial formula, n, stands for the number of times the experiment is performed. The second variable, p, represents the probability of one specific outcome. For example, lets suppose you wanted to know the probability of getting a 1 on a die roll. If you were to roll a die 20 times, the probability of rolling a one on any throw is 1/6. Roll twenty times and you have a binomial distribution of (n=20, p=1/6). SUCCESS would be roll a one and FAILURE would be roll anything else. If the outcome in question was the probability of the die landing on an even number, the binomial distribution would then become (n=20, p=1/2). Thats because your probability of throwing an even number is one half. Many instances of binomial distributions can be found in real life. For example, if a new drug is introduced to cure a disease, it either cures the disease (its successful) or it doesnt cure the disease (its a failure). If you purchase a lottery ticket, youre either going to win money, or you arent. Basically, anything you can think of that can only be a success or a failure can be represented by a binomial distribution.

A normal distribution, sometimes called thebell curve, is a distribution that occurs naturally in many situations. For example, thebell curveis seen in tests like the SAT and GRE. The bulk of students will score the average (C), while smaller numbers of students will score a B or D. An even smaller percentage of students score an F or an A. This creates a distribution that resembles a bell (hence the nickname). Thebell curveis symmetrical. Half of the data will fall to the left of the mean; half of the later will fall to the right. Many groups follow a Normal Distribution pattern. Thats why its widely used in business, statistics and in government bodies like theFDA: Heights of people. Measurement errors. Blood pressure. Points on a test. IQ scores. Salaries.

A normal distribution

A Binomial Distribution) shows either (S)uccess or (F)ailure.

Part 2Bil.StudentsWeight(kg)Height(cm)

1.Akmal Khalidah binti Hasan52157

2.Nurul Jannah binti Abdul Ghani52152

3.Nurzuriana binti Mohd Zahri56165

4.Nur Haflia Safika binti Mohd Sahari42152

5.Faiqah Adawiyah binti Yusoff42149

6.Nurin Jazlina binti Saeman53154

7.Afiqah binti Abd Aziz53152

8.Nur Ezatul Syazwani binti Mohd Ismail47151

9.Nur Syafawati binti Mohd Solleh49162

10.Nabila Hannah binti Deswir48158

11.Ainunul Khalilah binti Hasan 56152

12.Nur Aliyah binti Zaidi50157

13.Nurul Munirah binti Shamsudin54161

14.Nurul Nadiah binti Karim42147

15.Aina Safiqa binti Azhar53151

16.Aisyah Nazihah binti Nazri54153

17.Siti Hajar binti Ramli47159

18.Suhailah binti Sulaiman57156

19.Aliah Khaliqah binti Hasan55150

20.Nur Ahya Nadhira binti Nazri41154

21.Anisah Hamimi binti Zamri55160

22.Humaira Husna binti Ayob65152

23.Aisyatul Humaira binti Azmi44153

24.Nabilah Huda binti Ghazali45150

25.Nur Hairin Nizan binti Chairil43161

26.Wan Muhammad Akmal bin Wan Azman65183

27.Johan Ariff bin Rosdin58179

28.Muhammad Taufiq bin Othman70184

29.Muhammad Hafriz Najmi bin Nekmat87186

30.Ahmad Razin bin Azli58164

31.Muhammad Azrie bin Azman50164

32.Muhammad Amsyar Hakim bin Somad53158

33.Muhammad Sallehudin bin Tumijan62167

34.Ahmad Khairum Muzammil bin Hasan58164

35.Muhammad Syafiq bin Azmi75175

36.Muhammad Syahmi bin Safri63168

37.Muhammad Rafiq bin Azmi52168

38.Muhammad Arif Adli bin Mohd Azlan54159

39.Muhammad Zulfikri bin Lokman Hakim50164

40.Muhammad Syahmi Sufi bin Abdul Shukor77161

41.Ahmad Amir bin Ismail81176

42.Faiz Akmal bin Maiden53154

43.Muhammad Iqbal bin Seidi56162

44.Muhammad Hilmi bin Sawal60167

45.Muhammad Fikree bin Seidi59160

46.Luqman Al-Hakim bin Zainal57160

47.Khalid bin Al-Walid49152

48.Norsyahizi Haikal bin Mansor51163

49.Amirul Hakimi bin Ahmad66161

50.Muhammad Haziq Akmal bin Mohd72162

2(i) Mass (kg)FrequencyCummulative frequencyMidpointUpperboundryFxfx

1-10005.510.500

11-200015.520.500

21-300025.530.500

31-400035.540.500

41-50151545.550.5682.531053.75

51-60243955.560.5133273926

61-7064565.570.539325741.5

71-8034875.580.5226.617100.75

81-9025085.590.517114620.5

(ii) Mean , = (45.5 x 15 ) + (55.5 x 24) + (65.5 x 6) + (75.5 x 3) + (85.5x2)50= 2805 50= 56.1

Standard deviation, = - 56.1 = 10.08

(iii) Percentage of students with weight more than 60kg = = 223. i) Percentage of students with weight more than 60kg:

= 0.11 x 100 = 11

(ii) Percentage of students with weight less than 45 kg:

(iii) m

4) Normal distribution is more suitable when calculate the percentage of students.

5) P(X = 3) = C = 0.04247

6) = 0.3483

Part 3Bil.StudentsBMICategory

1.Akmal Khalidah binti Hasan21.1Normal

2.Nurul Jannah binti Abdul Ghani22.5Normal

3.Nurzuriana binti Mohd Zahri20.5Normal

4.Nur Haflia Safika binti Mohd Sahari18.2Underweight

5.Faiqah Adawiyah binti Yusoff18.9Normal

6.Nurin Jazlina binti Saeman22.3Normal

7.Afiqah binti Abd Aziz22.9Normal

8.Nur Ezatul Syazwani binti Mohd Ismail20.6Normal

9.Nur Syafawati binti Mohd Solleh18.7Normal

10.Nabila Hannah binti Deswir19.2Normal

11.Ainunul Khalilah binti Hasan 24.2Normal

12.Nur Aliyah binti Zaidi20.3Normal

13.Nurul Munirah binti Shamsudin20.8Normal

14.Nurul Nadiah binti Karim19.4Normal

15.Aina Safiqa binti Azhar23.2Normal

16.Aisyah Nazihah binti Nazri23.1Normal

17.Siti Hajar binti Ramli18.6Normal

18.Suhailah binti Sulaiman23.4Normal

19.Aliah Khaliqah binti Hasan24.2Normal

20.Nur Ahya Nadhira binti Nazri17.3Normal

21.Anisah Hamimi binti Zamri21.5Normal

22.Humaira Husna binti Ayob28.1Overweight

23.Aisyatul Humaira binti Azmi18.8Normal

24.Nabilah Huda binti Ghazali20.0Normal

25.Nur Hairin Nizan binti Chairil16.6Underweight

26.Wan Muhammad Akmal bin Wan Azman19.4Normal

27.Johan Ariff bin Rosdin18.1Underweight

28.Muhammad Taufiq bin Othman20.7Normal

29.Muhammad Hafriz Najmi bin Nekmat25.1Overweight

30.Ahmad Razin bin Azli21.6Normal

31.Muhammad Azrie bin Azman18.6Normal

32.Muhammad Amsyar Hakim bin Somad21.2Normal

33.Muhammad Sallehudin bin Tumijan22.2Normal

34.Ahmad Khairum Muzammil bin Hasan21.6Normal

35.Muhammad Syafiq bin Azmi24.5Normal

36.Muhammad Syahmi bin Safri22.3Normal

37.Muhammad Rafiq bin Azmi18.4Underweight

38.Muhammad Arif Adli bin Mohd Azlan21.4Normal

39.Muhammad Zulfikri bin Lokman Hakim18.6Normal

40.Muhammad Syahmi Sufi bin Abdul Shukor29.7Overweight

41.Ahmad Amir bin Ismail26.1Overweight

42.Faiz Akmal bin Maiden22.3Normal

43.Muhammad Iqbal bin Seidi21.3Normal

44.Muhammad Hilmi bin Sawal21.5Normal

45.Muhammad Fikree bin Seidi23.0Normal

46.Luqman Al-Hakim bin Zainal22.3Normal

47.Khalid bin Al-Walid21.2Normal

48.Norsyahizi Haikal bin Mansor19.2Normal

49.Amirul Hakimi bin Ahmad25.5Overweight

50.Muhammad Haziq Akmal bin Mohd27.4Overweight

2) (i) P ( X < 18.5 ) = P (z < 1) = 0.8413 = 0.1587 = 0.1587 = 17.8652 = 4

(ii) a) percentage of underweights students = = 8 b) percentage students with BMI more than 25 = = 12

3) (i) percentage of overweights students =

(ii) percentage students with BMI less than 18.5 = =0.1587 = 0.1587 X 100 = 15.87

(iii)

4)

5) Ways and strategies to reduce weight and live a healthier life :

Make appointments with your doctor and dentist.Catch up on your routine screening andimmunizations, and take the opportunity toask your doctorany questions you might have.

Gauge your girth.Measure your height and weight tocheck your BMI, andmeasure your waist circumferenceto see if you'reoverweightand if your waistline is putting your health at risk.

Assess your activity.How muchphysical activitydo you get in a typical week? How intense is that activity? How much variety do you get in your activity, and how much do you enjoy it? The CDC recommends that adults get at least two and a half hours per week of moderate-intensity aerobic activity or one hour and 15 minutes per week of vigorous-intensity aerobic activity, plus muscle-strengthening activities at least two days per week.

Keep a food diary.Write down everything you eat for a day -- and no fair skipping the items you're embarrassed about. "The idea is to write it down ... without judgment," says Kathianne Sellers Williams, MEd, RD, LD, a nutritionist,wellness coach, and personal trainer with Cafe Physique in Atlanta. "You can't change what you're not aware of or don't acknowledge."

Check your mood and energy.Healthy living includesemotional wellnessand adequate rest. How has your mood been lately? Are you experiencing anysymptoms of depressionoranxiety? Do you usuallysleepwell for seven to eight hours a night?

Further Exploration Johann Carl Friedrich GaussCarl Friedrich Gauss was born on 30 April 1777 inBrunswick (Braunschweig), in theDuchy of Brunswick-Wolfenbttel(now part ofLower Saxony,Germany), as the son of poor working-class parents.[3]His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before theFeast of the Ascension, which itself occurs 40 days afterEaster. Gauss would later solve this puzzle about his birthdate in the context offinding the date of Easter, deriving methods to compute the date in both past and future years.[4]He was christened andconfirmedin a church near the school he attended as a child.[5]Gauss was achild prodigy. There are many anecdotes about his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager. He completedDisquisitiones Arithmeticae, hismagnum opus, in 1798 at the age of 21, though it was not published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.Gauss's intellectual abilities attracted the attention of theDuke of Brunswick,[2]who sent him to the Collegium Carolinum (nowBraunschweig University of Technology), which he attended from 1792 to 1795, and to theUniversity of Gttingenfrom 1795 to 1798. While at university, Gauss independently rediscovered several important theorems;[6]his breakthrough occurred in 1796 when he showed that any regularpolygonwith a number of sides which is aFermat prime(and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and apowerof 2) can be constructed bycompass and straightedge. This was a major discovery in an important field of mathematics; construction problems had occupied mathematicians since the days of theAncient Greeks, and the discovery ultimately led Gauss to choose mathematics instead ofphilologyas a career. Gauss was so pleased by this result that he requested that a regularheptadecagonbe inscribed on his tombstone. Thestonemasondeclined, stating that the difficult construction would essentially look like a circle. The year 1796 was most productive for both Gauss and number theory. He discovered a construction of the heptadecagon on 30 March. He further advancedmodular arithmetic, greatly simplifying manipulations in number theory. On 8 April he became the first to prove thequadratic reciprocitylaw. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. Theprime number theorem, conjectured on 31May, gives a good understanding of how theprime numbersare distributed among the integers.Gauss also discovered that every positive integer is representable as a sum of at most threetriangular numberson 10 July and then jotted down inhis diarythe note: "! num=++". On October1 he published a result on the number of solutions of polynomials with coefficients infinite fields, which 150 years later led to theWeil conjectures.

ReflectionAdditional Mathematics

DIfferent from other subjects

Definitely challenging my mind and soul

It is not something we cant do because

Teacher is here to help us

. In getting the highest marks and

Of course us 5 Thaqofah will struggle to the end

Never say never to add. Maths but instead

All of us can say

Like this : I LOVE YOU LIKE A LOVE SONG, ADD MATHS

My, my

Actually, it has been two years since we studied together

The ups and downs we experienced

How I would miss those times next year

Everyone would, especially the Thaqopers

Memories after memories, tears after tears

Are what we cherish the most

Thank you for teaching us with patience

I, we, them. Lets pray and work hard until we succeed

Cause thats what Legacy of Licentiate wants

. . Sorry teacher.

XOXO, drmabet (@amalaey)