The diameter of bushings turned out by a manufacturing process is a normally distributed random variable with a mean of 4.035 mm and a standard deviation of 0.005 mm. A sample of 25 bushings is taken once an hour. (a) Within what interval should 95 percent of the bushing diameters fall? (b) Within what interval should 95 percent of the sample means fall? (c) What conclusion would you reach if you saw a sample mean of 4.020? A sample mean of 4.055?
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 diameter of bushings turned out by a manufacturing process is a normally distributed
random variable with a mean of 4.035 mm and a standard deviation of 0.005 mm. A sample
of 25 bushings is taken once an hour. (a) Within what interval should 95 percent of the
bushing diameters fall? (b) Within what interval should 95 percent of the sample means
fall? (c) What conclusion would you reach if you saw a sample mean of 4.020? A sample
mean of 4.055?
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