BIOM301 Chapter 6 Normal Probability Distributions Random Variables A variable x whose value depends on the outcome of a chance operation o 1 outcome per run of the chance operation o Every outcome is independent of every other outcome Two main groups o Discrete Random Variables Chapter 5 quantitative discrete o Continuous Random Variables Chapter 6 quantitative continuous Continuous Random Variable A quantitative continuous variable Ex Blood Pressure Just like for Discrete variables all outcomes determine by chance all outcomes are independent and only 1 outcome at a time Probability Distributions for Continuous Random Variables For Real Data any possible distribution could occur If you have lots of observations you can smooth out histograms bars into a probability distribution curve o Area under curve 1 reflects relative probabilities of events density curve Often but NOT ALWAYS is 1 symmetric 2 bell shaped Normal Curve Most measurement values tend to fall around the mean o If there is nothing else driving the distribution shape it will tend towards a normal shape Standard Normal Curve Table 3 o Mean 0 and standard deviation 1 o Table 3 contains the AREA under the standard normal curve between 0 and a specific value of z Area will be a decimal number between 0 and 0 5 o Used for finding Probabilities for Standard Normal Curve When finding normal distribution probabilities ALWAYS SKETCH IT OUT FIRST What is the probability that z is exactly equal to some number It s zero No difference because it s a normal distribution curve May be able to transform data that does not look normal Log transformation is common in biology Normal Approximation of the Binomial Sometimes when binomial distribution looks to be normal the binomial probabilities can be reasonably estimated using the normal probability distribution General Rule Normal distribution provides a reasonable approximation to a binomial probability when o n p 5 AND n 1 p 5 Comes in handy when n is very large
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