Presentation on theme: "Normal Distribution To understand the normal distribution To be able to find probabilities given the Z score To be able to find the Z score given the probability."— Presentation transcript:
Normal Distribution To understand the normal distribution To be able to find probabilities given the Z score To be able to find the Z score given the probability
Most commonly observed probability distribution 1800s, German mathematician and physicist Karl Gauss used it to analyse astronomical data Sometimes called the Gaussian distribution in science.
Normal Distribution Occurs naturally(e.g. height, weight,..) Centres around the mean Often called a bell curve
Normal Distribution Spread depends on standard deviation Percentage of distribution included depends on number of standard deviations from the mean
Properties of Normal Distribution Symmetrical Area under curve = 1
Standard Normal Distribution Mean ( =0 Standard deviation ( )=1
Standard Normal Distribution Z-scores are a means of answering the question ``how many standard deviations away from the mean is this observation?'' Tables are provided to help us to calculate the probability for the standard normal distribution, Z
Find P(Z<1.25) Tables give us P(Z
"name": "Find P(Z<1.25) Tables give us P(Z
Find P(Z>1.25) Tables give us P(Z1.25) = 1- 0.8944 = 0.1056
a) Find P(Z < 1.52) It is vital that you always sketch a graph b) Find P(Z > 2.60) c) Find P(Z < -0.75) d) Find P(-1.18 < Z < 1.43)
Your consent to our cookies if you continue to use this website.