A machine is designed to cut meter-sticks to be 1000 mm. long. 19 meter-sticks are measured, and it's found that they have a mean length of 1001.8 mm., with a standard deviation of 2.6 mm. To a 1% level of significance, can it be asserted that the standard deviation o of the process in general (i.e., of all the meter-sticks produced by the machine) is over 2 mm.?
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 is designed to cut meter-sticks to be 1000 mm. long. 19 meter-sticks are measured, and it's
found that they have a mean length of 1001.8 mm., with a standard deviation of 2.6 mm. To a 1%
level of significance, can it be asserted that the standard deviation o of the process in general (i.e., of
all the meter-sticks produced by the machine) is over 2 mm.?
[Assume that the lengths of all the meter-sticks are normally distributed.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed013cf4-4adc-4b56-b0c2-74e97b0a3744%2Fed1bd4d3-205f-4b5b-b81a-9d941ed63fd5%2F9jb133w_processed.jpeg&w=3840&q=75)
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