Empirical rule and Tchebychev rule a) Consider a mound shaped distribution, for which the empirical rule applies. Suppose the mean is (mu) = 45 and the standard deviation is (sigma) = 8 Find the percentage of the data found inside of each of the following intervals (29, 61) (37, 53) b) Suppose a distribution is irregularly shaped (in particular, not mound shaped). Suppose the mean in (mu) = 82 and the standard deviation is (sigma) = 12. Apply Tchebychev's inequality to give a minimum percentage for the percentage of the data found in the following interval. (64, 100) What interval will guarantee at least 88.9% of the data is inside the interval (symmetric about the mean (mu) The interval will have the form ( (mu) - k (sigma), (mu) + k (sigma) ) Find the value for k.
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) Consider a mound shaped distribution, for which the empirical rule applies.
Suppose the mean is (mu) = 45 and the standard deviation is (sigma) = 8
Find the percentage of the data found inside of each of the following intervals
(29, 61)
(37, 53)
b) Suppose a distribution is irregularly shaped (in particular, not mound shaped).
Suppose the mean in (mu) = 82 and the standard deviation is (sigma) = 12.
Apply Tchebychev's inequality to give a minimum percentage for the percentage of the data found in the following interval.
(64, 100)
What interval will guarantee at least 88.9% of the data is inside the interval (symmetric about the mean (mu)
The interval will have the form ( (mu) - k (sigma), (mu) + k (sigma) )
Find the value for k.
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