There are two machines available for cutting corks intended for use inwine bottles. The first produces corks with diameters that are normallydistributed with mean 3 cm and standard deviation .1 cm. The secondmachine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation .02 cm. Acceptable corkshave diameters between 2.9 cm and 3.1 cm. Which machine is morelikely to produce an acceptable cork?
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!
There are two machines available for cutting corks intended for use in
wine bottles. The first produces corks with diameters that are
distributed
machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation .02 cm. Acceptable corks
have diameters between 2.9 cm and 3.1 cm. Which machine is more
likely to produce an acceptable cork?
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