In a study of intelligence, the time (in seconds) for a laboratory animal to reach a reward in a maze was found to have a probability density function 12 f(t) t> 12 t2 where 12 seconds is the minimum time to traverse the maze. (a) Find the probability that an animal chosen at random takes between 54 and 108 seconds. (b) Find the probability that an animal chosen at random takes more than 54 seconds given that it took less than 108 seconds.
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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