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Unformatted text preview: Statistics 100 Midterm Spring 2012 7 March 2012 Solutions 1. Short answer questions . (a) IQR = 106- 96 = 10 ; (1 . 5)( IQR ) = 15 , so the lower outlier boundary is 96- 15 = 81 . 82 is inside the boundary and is not an outlier. (b) Using the tables of the standard Normal distribution, the lower 25% of a standard Normal is between- . 67 and- . 68 . It is ok to use either one of these values in the solution. Using- . 67 the value on the distribution of interests will be x = + z = 3- (0 . 5)(0 . 67) = 2 . 67 . The lower 25% of the distribution of interest rates is 2 . 67% . (c) False. In a left skewed distribution, the mean will be pulled down by the small values and will typically be smaller than the median. (d) You can use the standard Normal variable Z for this, since the probability of being 2 . 5 standard deviations below the mean is the same for all Normal distributions. Using the tables of the standard Normal, Pr( Z <- 2 . 5) = 0 . 0062 ....
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