A. The following table shows the number of home runs hit by leaders in the category for the national league during the Zambia Major league Baseball Season. The mean of the data is 37.9 and standard deviation is 11. Sorted National League Home Run Leaders 73 64 57 49 49 45 41 39 38 38 37 37 37 36 36 34 34 34 34 34 33 31 31 30 30 29 27 27 27 25
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!
(i) Verify that Chebyshev’s Theorem holds true for two standard deviations
around the
(ii) Verify that Chebyshev’s Theorem holds true for three standard deviations
around the mean.
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