1. Birth weights of babies in the United States can be modeled by a normal distribution with mean 3250 grams and standard deviation 550 grams. Those weighing less than 2500 grams are considered to be of low birth weight. (a) Sketch a normal distribution curve and shade in the region whose area corresppnds to the probability that a baby will have a low birth weight. (The prohalailety that binth weigh is less than 2500=.08634 3250 -SSO density 2700 2760 (b) Based on this shaded region (using the Empirical Rule and remembering that the total area under the normal curve is 1), make an educated guess for the proportion of babies born with a low birth weight. (c) Using Excel, find the proportion of babies born with a low birth weight. How did your computed answer compare to your educated guess?
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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