Bottled Drinking Water Americans drank an average of 23.2 gallons of bottled water per capita in 2004 . If the standard deviation is 2.7 gallons and the variable is normally distributed, find the following probabilities. Use a graphing calculator and round the answers to four decimal places. Part: 0 / 2 0 of 2 Parts Complete Part 1 of 2 More than 28 gallons of bottled water. P more than 28 gallons of botted water = ??
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Bottled Drinking Water Americans drank an average of
More than
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P
28
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??
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Given Information:
Americans drank an average of 23.2 gallons of bottled water. i.e.,
Standard deviation 2.7 gallons.
To find the probability that a randomly selected American drank more than 28 gallons of bottled water:
Let X denote the bottled water in gallons drank by an American.
Z-score is a measure which tells how many standard deviations away, a data value is, from the mean.
It is given by the formula:
Standardize X = 28 by substituting the values in the formula:
Required probability is obtained as follows:
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