STAT 1000 Lecture Notes - Lecture 29: Random Variable, Standard Deviation, Central Limit Theorem

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Even though we don"t know the form of the distribution of diameters, since the sample size is high, we know that the distribution of x is approximately normal. ( 0. 05 100. 1. 24 1. 25 < z < 0. 05 100. We can"t calculate this probability! we don"t know the form of the distribution of x, and the sample size is not high enough to use the central limit theorem. In the previous unit you were introduced to the binomial distribution and the points that need to be satisfied in order for a variable to be considered binomial. In sampling we like to estimate the proportion of successes our estimator is: Does not have a binomial distribution because it is not a count. If the sample size is much smaller than the size of a population with proportion p of successes, then the mean and standard deviation of are:

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