normal curve

CHARACTERISTICS OF THE NORMAL PROBABILITY DISTRIBUTION

JOMER D.L. ARTILLERO

Math Teacher

Prayer

Amang Banal, Dakila at Makapangyarihan sa lahat. Salamat sa mga biyayang ipinagkakaloob mo sa amin. Salamat din po sa patuloy Mo pong pagliligtas sa amin, lalo na sa pandemyang nararanasan ng mundo. Nawa'y samahan Mo po ang aming mga paggawa sa araw na ito. At patawarin Mo po ang aming mga kasalanan, kung paanong kami ay nagpatawad na sa mga nagkasala sa amin. Lahat ng ito'y hinihiling namin sa pangalan ng Iyong Anak na si Cristo Hesus. Amen

Multiple Choice

HOW ARE YOU FEELING TODAY?

House Rules

• Be ready to learn and to participate

• Be honest and respectful

• Ask questions if in doubt

• Use gadgets responsibly, if permitted

Euler's Number (e)

Euler's number is an important constant that is found in many contexts and is the base for natural logarithms. An irrational number represented by the letter e, Euler's number is 2.71828..., where the digits go on forever in a series that never ends or repeats (similar to pi).

​https://www.investopedia.com/terms/e/eulers-constant.asp

Multiple Choice

the quality of being made up of exactly similar parts facing each other or around an axis.

• aysmptote

• curve

• frequency

• normal

• symmetry

Symmetry

​https://www.cuemath.com/geometry/symmetry/

Symmetry

​https://en.wikipedia.org/wiki/File:Marikina-city-hall-2012-01.jpeg

Multiple Choice

conforming to a standard; usual, typical, or expected.

• aysmptote

• curve

• frequency

• normal

• symmetry

Normal

Multiple Choice

the rate at which something occurs or is repeated over a particular period of time or in a given sample.

• aysmptote

• curve

• frequency

• normal

• symmetry

Frequency

​https://thirdspacelearning.com/gcse-maths/statistics/frequency-table/

Multiple Choice

a line or curve that acts as the limit of another line or curve.

• aysmptote

• curve

• frequency

• normal

• symmetry

Asymptote

​https://byjus.com/maths/asymptotes/

​https://www.mathsisfun.com/algebra/asymptote.html

PULSE RATE

To find your pulse, use two fingers (your middle and your index fingers) to find your carotid artery, just below your esophagus or throat. You can find it also at the base of your hand (we call it the pulse). Then, count the beats you feel for 20 seconds. Multiply that number by three. That’s roughly the number your heart beats per minute. Put it in the google sheet provided.

 From <https://www.mdanderson.org/publications/focused-on-health/how-to-get-your-hear-rate-up.h23Z1592202.html>

Open Ended

Why do we need to know how to get our pulse rates?

Open Ended

What do the y-axis represent?

Open Ended

What do the x-axis represent?

Open Ended

Which pulse rate has the highest frequency?

Open Ended

As we go to the left of the graph, what happens

Open Ended

If we get the pulse rate of a learner from another Grade 11 student, can you get an estimate as to where will it be in the graph? Explain your answer.

Curves & Equations in Real-life

Curves & Equations in Real-life

Do you see any familiar symbols?

Are you familiar with the curve of this equation?

Do anyone have an idea what this curve is called?

What are the uses of this curve?

Curves & Equations in Real-life

Curves & Equations in Real-life

Let us see the graph, called histogram, of all midterm scores of Grade 11 in Statistics and Probability.

 

Open Ended

Is it similar to the graph of your pulse rates?

Open Ended

Does it look like a circle, square or a parabola? What shape or object can you compare it with?

Definition

A normal distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve.

Normal Distribution

No variable fits a normal distribution perfectly, since a normal distribution is a theoretical distribution. However, a normal distribution can be used to describe many variables, because the deviations from a normal distribution are very small.

Normal Distribution

Circles can be different sizes, depending on their diameters (or radii), and can be used to represent wheels of different sizes.

Normal Distribution

Likewise, normal curves have different shapes and can be used to represent different variables. The shape and position of a normal distribution curve depend on two parameters, the mean and the standard deviation.

Normal Distribution

Multiple Choice

What happens to the normal curve if we INCREASE the mean?

• Goes up

• Goes down

• Goes left

• goes right

Multiple Choice

What happens to the normal curve if we DECREASE the mean?

• Goes up

• Goes down

• Goes left

• goes right

Multiple Choice

What happens to the normal curve if we INCREASE the STANDARD DEVIATION?

• It becomes lower and wider

• It becomes higher and narrower

• It becomes lower and narrower

• It becomes higher and wider

Multiple Choice

What happens to the normal curve if we DECREASE the STANDARD DEVIATION?

• It becomes lower and wider

• It becomes higher and narrower

• It becomes lower and narrower

• It becomes higher and wider

ILLUSTRATIONS

Characteristics of Normal Distribution

Characteristics of Normal Distribution

​1. A normal distribution curve is bell-shaped.

Characteristics of Normal Distribution

Characteristics of Normal Distribution

2. The mean, median, and mode are equal and are located at the center of the distribution.

Characteristics of Normal Distribution

Characteristics of Normal Distribution

3. It is symmetric about the mean.

Characteristics of Normal Distribution

Characteristics of Normal Distribution

4. The normal curve asymptotic to the horizontal axis. (it approaches, but never touches, the x-axis as it extends farther and farther away from the mean).

Characteristics of Normal Distribution

5. The total area under a normal distribution curve is equal to 1.00, or 100%.

Characteristics of Normal Distribution

6. The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68, or 68%; within 2 standard deviations, about 0.95, or 95%; and within 3 standard deviations, about 0.997, or 99.7%.

Characteristics of Normal Distribution

1.    A normal distribution curve is bell-shaped.

2.    The mean, median, and mode are equal and are located at the center of the distribution.

3.    It is symmetric about the mean.

4.    The normal curve asymptotic to the horizontal axis. (it approaches, but never touches, the x-axis as it extends farther and farther away from the mean).

5.    The total area under a normal distribution curve is equal to 1.00, or 100%.

6.    The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68, or 68%; within 2 standard deviations, about 0.95, or 95%; and within 3 standard deviations, about 0.997, or 99.7%.

FORMATIVE ASSESSMENT

PERFORMANCE TASKS (GROUPINGS)

YELLOW TEAM

 

1.    List down of at least 3 properties a normal distribution.

2.    Draw a normal curve with µ=20, and σ=7

3.    Label the graph within 1 standard deviation and indicate its percentage.

ORANGE TEAM

 

1.    List down at least 5 properties a normal distribution.

2.    Draw two normal curves with µ=10, but with different σ (standard deviations). Be sure to indicate what σ you used.

3.    Using the graph in #2, with the greater standard deviation, divide the graph within two standard deviations and label the percentages accordingly.

RED TEAM

 

1.    List down at least 6 properties a normal distribution.

2.    1.    Draw two normal curves with the different µ (means), but with same σ (standard deviations). Be sure to indicate what µ & σ you used.

3.    Using the graph in #2, with the greater mean, divide the graph within three standard deviations and label the percentages accordingly.