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The height of the water level in mineral water bottles has a mean of 140 mm and a standard deviation of 4 mm. Assume that the height of the water level is normally distributed and water levels in different bottles are independent.
(a) Determine the probability that the average height of the water level of 9 bottles is between 138 mm and 142 mm.
(b) Determine the minimum number of bottles that need to be measured such that the probability that the average height exceeds 142 mm is less than or equal to 0.1.
If Chebychev Inequality gives the lower bound for probability. For the present problem the lower bound for the probability is 0.75 and actual probability is 0.87.
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Suppose that the number of cars, X, that pass through a car wash between 4:00pm and 5:00pm on any sunny Friday has the following probability distribution:
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