An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have been less than 240 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father? Calculate the z-scores first, and then use those to calculate the probability. 5. A study shows that employees that begin their work day at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. What is the probability that a randomly chosen employee reports to work between 9:00 and 9:10? Please show your work as well as the graph of the distribution.
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!
4. An expert witness for a paternity lawsuit testifies that the length of a pregnancy is
5. A study shows that employees that begin their work day at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. What is the probability that a randomly chosen employee reports to work between 9:00 and 9:10? Please show your work as well as the graph of the distribution.
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