lecture_08_f01

# lecture_08_f01 - Statistics 400 Lecture 8 Completed so...

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Statistics 400 - Lecture 8

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Completed so far (any material discussed in these sections is fair game): 2.1-2.5 4.1-4.5 5.1-5.8 (READ 5.7) 6.1-6.4; 6.6 7.1-7.2 Today: finish 7.3, 8.1-8.3 READ 7.4!!! Assignment #3: 6.2, 6.6, 6.34, 6.78 (interpret the plot in terms of Normality), 7.20,  7.28, 8.14, 8.22, 8.36 Due: Tuesday, Oct 16
Central Limit Theorem In a random sample (iid sample) from any population with mean      and standard deviation     when n is large, the distribution of the  sample mean     is approximately normal. That is, Thus,  μ σ x n x Z / σ μ - =

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Implications So, for random samples, if have enough data, sample mean is  approximately normally distributed...even if data not normally  distributed If have enough data, can use the normal distribution to make  probability statements about  x
Example A busy intersection has an average of 2.2 accidents per week with  a standard deviation of 1.4 accidents Suppose you monitor this intersection of a given year, recording the  number of accidents per week. Data takes on integers (0,1,2,...) thus distribution of number of  accidents not normal. What is the distribution of the mean number of accidents per week  based on a sample of 52 weeks of data

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Example What is the approximate probability that     is less than 2 What is the approximate probability that there are less than 100  accidents in a given year?  x
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