Statistics_6 - Chapter 6: The Normal Distribution •...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 6: The Normal Distribution • Normal Distributions • Applications of the Normal Distribution • The Central Limit Theorem • The Normal Approximation to the Binomial Distribution. The Normal Distribution : • A normal distribution is a continuous, symmetric, bell-shaped distribution of a variable with curve equation g1877 g3404 1 g2026 2g2024 g1857 g2879 g2869 g2870g3097 g3118 g4666g3051g2879g3091g4667 g3118 where μ is the population mean and σ is the standard deviation. The Properties of the Theoretical 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. A normal distribution curve is unimodal. 4. The curve is symmetric about the mean. 5. The curve is continuous ; that is, there are no gaps or holes. For each value of X , there is a corresponding value of Y. 6. The curve never touches the x axis . 7. The total area under a normal distribution curve is equal to 1.00 , or 100%. 8. 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%. The standard Normal distribution: • The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, i.e. has eq. g1877 g3404 1 2g2024 g1857 g2879g3051 g3118 Note: any normally distributed variable x can be transformed to a standard normal variable z using the transformation g1878 g3404 g3051g2879g3091 g3097 . • Table E in Appendix C gives the area under the standard normal curve to the left of any z value from -3.49 to 3.49 . Finding Areas Under (the probability) the Standard Normal Distribution Curve: 1. To the left of any z value: Look up the z value in the table and use the area given . 2. To the right of any z value: Look up the z value and subtract the area from 1. 3. Between any two z values: Look up both z values and subtract the corresponding areas. Important: The area under the normal curve within two values (a,b) equals the probability that the normal variable x takes values within these two values (a,b)....
View Full Document

Page1 / 21

Statistics_6 - Chapter 6: The Normal Distribution •...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online