The alcohol content of wine depends on the grape variety, the way in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 16 winemakers in the same region of Italy: 12.86 12.88 12.81 12.70 12.51 12.60 12.25 12.53 13.49 12.84 12.93 13.36 13.52 13.62 12.25 13.16 Give a 95% confidence interval for the mean alcohol content of wine of this type.
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!
- The alcohol content of wine depends on the grape variety, the way in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 16 winemakers in the same region of Italy:
12.86 12.88 12.81 12.70 12.51 12.60 12.25 12.53 13.49 12.84
12.93 13.36 13.52 13.62 12.25 13.16
Give a 95% confidence interval for the mean alcohol content of wine of this type.
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