The bones of a newly discovered dinosaur weigh 170 pounds and measure 9 feet, with a 6-inch claw on one toe of each hind foot. The age of the dinosaur was estimated using a radioactive substance dating of rocks surrounding the bones. Complete parts a and b. a. The radioactive substance decays exponentially with a half-life of approximately 1.23 billion years. Use the fact that after 1.23 billion years a given amount of the radioactive substance will have decayed to half the original amount to show that the decay model for the radioactive substance is given by A = An - 0.56353t where t is in billions of years. e To show that the decay model for the radioactive substance is A = An e - 0.56353t find the decay rate k for a substance. Substitute the values of A and t in the exponential decay model, A = A, e kt A = A, e kt V = A, e 1.23k Substitute.
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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