Lecture4.sec.5.1

Lecture4.sec.5.1 - Lecture 4 Section 5.1 Sample Means In...

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Lecture 4, Section 5.1 Sample Means In section 1.3, we learned how to use the normal distribution for X if we knew the μ and σ and if X was normally distributed. Now, we will see how to use the normal distribution for sample means. Remember, the Normal distribution for X ? What is X? X is a single observation of a variable we are interested in (ie. a score or account balance or height or weight or grade). When do we use normal distribution? Use if X is normally distributed. Mean and standard deviation of X: μ and σ (told to us in the problem) We standardize using this formula for Z: X Z μ σ - = A population distribution of any variable, X, is the distribution of the values X takes for all members of the population. The population distribution is also the probability distribution of any variable, X, when we choose one individual observation from the population at random. To use a normal distribution to describe sample means we will use the principle that a statistic from a random sample or randomized experiment is itself a random variable. The probability distribution of the statistic is its sampling distribution .
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