Normal Distribution and its characteristics.pptx

presentation for statistics and probability grade 11 - normal distribution and its characteristics

1. The Normal Distribution and Its Properties

2. NORMAL DISTRIBUTION Is a probability distribution of continuous random variables. It shows a graphical representations of obtained through measurement such as height and weight of the students . It is also known as Gaussian Distribution and sometimes called the Bell Curve . It is used to describe the characteristics of a populations and help us visualize the inferences we make about the population. It is also used to determine the probabilities and percentile of the continuous random variables in the distribution. 3

3. 4

4. 5

5. Properties of a Normal Distribution / Normal Curve 6 Distribution curve is bell-shaped. The curve is symmetrical about its center . This means that, if we draw segment from the peak of the curve down to the horizontal axis, the segment divides the normal into two equal parts or areas. The mean, median and mode coincide at the center . This also means that in the normal distribution, or distribution described by normal curve, the mean, median, mode are equal.

6. 7 4. The width of the curve is determined by the standard deviation of the distribution. 5. The tails of the curve are plotted in both direction and flatten out indefinitely along the horizontal axis. The tails are thus asymptotic to the baseline. A portion of the of the graph that is asymptotic to the reference axis or another graph is called an asymptote, always approaching one another but never touching it. Properties of a Normal Distribution / Normal Curve Standard deviation Has small value Standard deviation Has large value

7. 8 6 . The total area of a normal curve is 1. This means that the normal curve represents probability, or the proportion, or the percentage associated with specific set of measurement values. Properties of a Normal Distribution / Normal Curve

8. 9 are the points that mark the change in the curve’s concavity . the point at which a change in the direction of curve at mean minus standard deviation and mean plus standard deviation . Note that each inflection point of the normal curve is one standard deviation away from the mean. Inflection Point

9. 10

10. Let’s try this! 12 Sketch the normal curve of each distribution Mean = 95, Standard deviation = 12 Mean = 60 ; Standard deviation = 6 Mean = 23.8; Standard deviation = 5.2

11. Let’s try this! 14 A continuous random variable X is normally distributed with a mean of 45 and standard deviation of 6 . Find the percentage of the following: P( 39 < X > 51) P ( X > 45) P ( X < 39)

12. Evaluation 16 Multiple Choice. Choose the letter of the best answer. 1. What is another name for normal distribution? A . Gaussian distribution B . Poisson distribution C . Bernoulli’s distribution D . Probability distribution 2. What is the total area in the distribution under the curve? A . 0 B . 1 C . 2 D . 3

13. Evaluation 17 Multiple Choice. Choose the letter of the best answer. 3. What marks the change in the curve’s concavity? A . curve B . inflection points C . mean D . standard deviation 4. Which value is found at the center of the normal curve? A . mean B . median C . mode D . all of the above

14. Evaluation 18 Multiple Choice. Choose the letter of the best answer. 5. Which of the following is a parameter of normal distribution? A. mean B. standard deviation C. mean and standard deviation D. none of the above 6. Which of the following symbols is used to denote the mean? A.ó B. μ C. α D. ∞

15. Evaluation 19 Multiple Choice. Choose the letter of the best answer. 7. Which of the following does not describe a normal curve? A. asymptotic B. bell-shaped C. discrete D. symmetrical about the mean 8. What percent of the area under a normal curve is within 2 standard deviations? A. 68.3% B. 95.4% C. 99.7% D. 100%

16. Evaluation 20 Multiple Choice. Choose the letter of the best answer. 9. What percent of the area under a normal curve is within 1 standard deviation? A. 68.3% B. 95.4% C. 99.7% D. 100% 10. What percent of the area under a normal curve is within 3 standard deviations? A. 68.3 % C. 99.7 % B. 95.4 % D. 100%

17. Additional Activity 21 Directions: Make a sketch for each of the 3 areas under the normal curve as stated in the empirical rule. Using a mosaic art, shade the area that corresponds to the area under the normal curve. You may use eggshells, old magazines, dried leaves or any materials available at home.