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# Zinfandel is a popular red wine varietal produced almost ISBN: 9780321629111 32

## Solution for problem 47E Chapter 1

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 47E

Zinfandel is a popular red wine varietal produced almost exclusively in California. It is rather controversial among wine connoisseurs because its alcohol content varies quite substantially from one producer to another. In May 2013, the author went to the website klwines.com randomly selected 10 zinfandels from among the

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Answer: Step1: The given values of alcohol (%) is 14.8 14.5 16.1 14.2 15.9 13.7 16.2 14.6 13.8 15.0 Step2: a). Here we need to calculate measures of center (mean and median) of the data. X 14.8 14.5 16.1 14.2 15.9 13.7 16.2 14.6 13.8 15 x = 148.8 The formula for mean is given by i Mean x = 148.8 n = 10 = 14.88 Therefore, the mean alcohol content in red wine is 14.88 %. The formula for median is given by For n is odd: th Median = ( n + ) observation. 2 For n is even: Average of ( ) thand (n + 1) th observation. 2 2 The given data is 14.8 14.5 16.1 14.2 15.9 13.7 16.2 14.6 13.8 15.0 Here n = 10, it is even. So the median is the average of 5th and 6th observations. i.e., median = (15.9 + 13.7) 2 = 14.8 Therefore, the median alcohol content in red wine is 14.8 %. Step3: b). To calculate the sample variance. 2 Variance s = (xx) n 1 (x x) X 14.8 0.0064 14.5 0.1444 16.1 1.4884 14.2 0.4624 15.9 1.0404 13.7 1.3924 16.2 1.7424 14.6 0.0784 13.8 1.1664 15 0.0144 x = (x x)2 = 7.536 148.8 (xx) Variance s = n 1 = (7.536) 10 1 Variance s = 0.8373 Therefore the sample variance s = 0.8373. Step4: c). To calculate sample variance using shortcut formula. First we have to subtract 13 from each observation. These are, 1.8, 1.5, 3.1, 1.2, 2.9, 0.7, 3.2, 1.6, 0.8, 2. 2 (x x) X 1.8 0.0064 1.5 0.1444 3.1 1.4884 1.2 0.4624 2.9 1.0404 0.7 1.3924 3.2 1.7424 1.6 0.0784 0.8 1.1664 2 0.0144 2 x = (x x) = 18.8 7.536 xi x = 18.8 = 10 x = 1.88 2 2 (xx) Variance s = n 1 (7.536) = 10 1 s = 0.8373. Subtracting 13 from each value will not affect the variance.

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##### ISBN: 9780321629111

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Zinfandel is a popular red wine varietal produced almost