Weights (in pounds) of Regular Coke are listed below. Although the mean and standard deviation are sample statistics, assume that they are population parameters for all cans of regular Coke. 0.8192 0.8251 0.8247 0.8189 0.8152 0.8264 0.8126 0.8194 0.8163 0.7901 0.8295 0.8176 0.8194 0.8244 0.8244 0.8284 0.8211 0.8073 0.8161 0.8165 0.8110 0.8079 0.8192 0.8143 0.8207 0.8044 0.8062 0.8150 0.8150 0.8170 0.8128 0.8229 0.8181 0.8161 0.8172 0.8152 a. Determine the mean and standard deviation of the weights of regular coke. Use the sample standard deviation formula. b. If a can of regular Coke is randomly selected, find the probability that its contents weigh more than 0.8300 lb. For purposes of monitoring Coke production in the future, find the weights separating the bottom 10% and top 10%. С.
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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