The mean value of a can of super soda is 12 ounces, with a standard deviation of 0.6 ounces. the volumes of all cans of super soda are normally distributed. a) between what two values do 95% of the volumes of cans of soda lie? b) A random sample of 36 cans of soda is drawn. what is the probability of a can of super soda contains less than 11.8 ounces? c) for a random sample of 36 cans, what percent of cans of super soda contains less than 12.1 ounces?
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!
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a) between what two values do 95% of the volumes of cans of soda lie?
b) A random sample of 36 cans of soda is drawn. what is the probability of a can of super soda contains less than 11.8 ounces?
c) for a random sample of 36 cans, what percent of cans of super soda contains less than 12.1 ounces?
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