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An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

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Given a binomial distribution variable with n=20 and p=0.60 find the following possibilities using the binomial table a) p(x < 13) b) p x > 15) c) p(x = 17) d) p(11 < x < 14) e) p(11 < x < 14)