A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced standard deviation 0.1 cm. The specifications call for corks with diameters between 3.9 and 4.1 cm. A cork not meeting the specifications is considered defective. (A cork that is too small leaks and causes the wine to deteriorate; a cork that is too large doesn't fit in the bottle.) What proportion of corks produced by this machine are defective? (Round your answer to four decimal places.) well approximated by a normal distribution with mean 4 cm and A USE SALT You may need to use the appropriate table in the appendix to answer this question.
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!
![A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 4 cm and
standard deviation 0.1 cm. The specifications call for corks with diameters between 3.9 and 4.1 cm. A cork not meeting the specifications is considered defective. (A cork that is too small leaks and
causes the wine to deteriorate; a cork that is too large doesn't fit in the bottle.) What proportion of corks produced by this machine are defective? (Round your answer to four decimal places.)
A USE SALT
You may need to use the appropriate table in the appendix to answer this question.
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