The lengths of bolts produced in a factory may be taken to be normally distributed. The botlts are checked on two "go-no go" gauges and those shorter tthan 2.9 or longer than 3.1 inches are rejected. A random sample of 50 bolts are checked. If the n1 = 12 and n2 = 12, estimate the mean and the standard deviation for these bolts. State your assumptions. n1 being the number of bolts below 2.9 and n2 is the number of bolts above 3.1.
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 lengths of bolts produced in a factory may be taken to be
As the data is being assumed to be following Normal Distribution, we may want to consider the probability using Standard Normal Variate.
Let X be the size of the bolts (Drawn from the sample of size 50).
For Probability that the number of bolts below 2.9 is given as P(X<2.9). Now
Where is the sample Mean (i.e. 12) and is sample Standard Deviation(i.e 12).
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