EPHD203 Lecture 8 Fall 2024 Normal Distribution PDF

EPHD203: Lecture 8: Normal Distribution and the standard normal curve...

EPHD203: Lecture 8: Normal Distribution and the standard normal curve C O UR S E INST RUCTOR S D R. M O N I Q U E C H A AYA , D R. P H J O S L E E N A L B A R AT H I E , P H D ( S ) Acknowledgment: Slides provided by Khalil El Asmar, PhD & Lilian Ghandour, PhD Session Learning Objectives Understand the properties of the normal distribution Compute Z-scores Understand the concept of the Central Limit Theorem Normal Distribution Model for continuous outcome Mean=median=mode  Normal distribution The normal distribution is defined by its probability density function (or It makes life a pdf), which is given as lot easier for us 1  1 2 f ( x) = exp  − 2 ( x −  )  −  x   if 2  2  we standardize for some parameters μ (mean of the normal distribution), σ (standard our normal deviation of the normal distribution) with σ > 0 curve, with a mean of zero The density function follows a bell-shaped curve. and a standard The curve is symmetric about the mean μ. deviation of 1 A normal distribution with mean μ and variance σ2 is referred to as an unit. N(μ, σ2 ) distribution 4  Normal Distribution Notation: m=mean and s=standard deviation −3 −2 −  + +2 +3  Normal Distribution Properties of Normal Distribution I) The normal distribution is symmetric about the mean (i.e., P(X > ) = P(X < ) = 0.5). ii) The mean and variance,  and 2, completely characterize the normal distribution. iii) The mean = the median = the mode. P( -  < X <  + ) = 0.68, P( - 2 < X <  + 2) = 0.95, P( - 3 < X <  + 3) = 0.99 iv) P(a < X < b) = the area under the normal curve from a to b. Example 5.11.Normal Distribution Body mass index (BMI) for men age 60 is normally distributed with a mean of 29 and standard deviation of 6. What is the probability that a male has BMI less than 29? Example 5.11.Normal Distribution P(X