AEM 201 1st Edition Lecture 13PREVIOUS LECTUREI. Continuous Probability DistributionsII. Some Important Continuous Probability DistributionsCURRENT LECTUREI. Some Important Continuous Probability II. Assessing NormalitySOME IMPORTANT CONTINUOUS PROBABILITY• The standard normal distribution is symmetric at 0 and has a standard deviation of 1• The probability of one number occurring is 0, so if you include a number in a range or not does not matter• Always draw the picture the picture when answering questions using the cumulative probabilities for the standard normal distribution table • The probability of an exact point is always zero in a continuous distribution• Z-Transformation: mathematical means by which any normal random variable with a mean and a standard deviation can be converted into standard normal• To make the mean equal to 0 we simply subtract the mean from each observation in the population• To then make the standard deviation equal to one, we divide the results in the first step by the standard deviation• The resulting transformation is given byo Z=(x-)/• Why is the normal probability distribution considered so importanto Many random variables are naturally normally distributedThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o Many distributions, such as the Poisson and the binomial, can be approximated by the normal distributiono The distribution of many statistics, such as the sample mean and the sample proportion are approximately normally distributed if the sample is sufficiently large (Central Limit Theorem)ASSESSING NORMALITY• Unlike many common probability distributions (such as the Poisson, exponential, binomial, hypergeometricetc) random variables that are the normally distributed do not have specific characteristics that make them easy to identify• Because of this we often resort to using sample data to attempt to assess the normality of the population from which the sample has been
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