The time between infection and the display of symptoms for streptococcal sore throat is a random variable whose probability density function can be approximated by the following. f(t) = 1 15,676 t2e−0.05t if 0 ≤ t ≤ 150 and f(t) = 0 otherwise (t measured in hours) (a) What is the probability that an infected patient will display symptoms within the first 72 hours? (Round your answer to three decimal places.) (b) What is the probability that an infected patient will not display symptoms until after 60 hours? (Round your answer to three decimal places.)
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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