Use the Empirical Rule. (Do not use technology. Technology will give a slightly different answer.) Draw a sketch of the normal distribution and label the mean and 1, 2, and 3 standard devitons above and below the mean with computed values. Assume that the weight of 1-year-old girls in the USA is normally distributed with Mean = 9.5 kg, Standard Deviation = 1.1 kg. %3! %3D (a) 68% of the data is between which 2 values? kg -- kg (b) 95% of the data is between which 2 values? kg -- kg (c) What percentage of the data is less than 8.4 kg? (d) What percentage of the data is between 7.3 kg and 11.7 kg? (w) What percentage of the data is more than 12.8 kg?
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!
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