a) rejected whereas the mean strength is actually 5000 kg=cm2 b) accepted whereas the mean strength is actually 4960 kg=cm2
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!
Engineers claims that a certain formula can increase the strength, X, of concrete with mean
5000 kg=cm2 and standard deviation 120 kg=cm2. To test the hypothesis = 5000 kg=cm2
against the alternative < 5000 kg=cm2, a sample of 50 concrete slabs are tested for their
strength. The rejection region the hypothesis test is x < 4970. Find the probability that the
claim is
a) rejected whereas the mean strength is actually 5000 kg=cm2
b) accepted whereas the mean strength is actually 4960 kg=cm2
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