A computer program generates a random number to simulate a user's reaction time, which is known to lie between 200 and 500 milliseconds, with all values in that range equally likely.Which probability distribution is most appropriate for modeling the reaction time?

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BlackTom AI · Accepted Answer

Consider the scenario: a computer program samples a reaction time that can take any value between 200 and 500 milliseconds, and every value in that interval is equally likely.
Option a: Geometric distribution. This models the number of trials until the first success in a sequence of independent Bernoulli trials, not a continuous time measurement. It is inappropriate for representing a continuous reaction time.
Option b: Uniform distribution. This precisely matches the description: a continuous distribution where all outcomes in the interval [200, 500] milliseconds are equally probable.
Option c: Poisson distribution. This is a discrete distribution typically used for counting the number of events in a fixed interval when events occur with a known average rate. It does not model a continuous reaction time with equal likelihood over an interval.
Option d: Binomial distribution. This describes the number of successes in a fixed number of independent Bernoulli trials, a discrete count, not a continuous time value.
In light of these characteristics, the only distribution that aligns with a continuous range of values with equal likelihood is the uniform distribution, specifically a continuous uniform distribution on [200, 500].

A computer program generates a random number to simulate a user's reaction time, which is known to lie between 200 and 500 milliseconds, with all values in that range equally likely.Which probability distribution is most appropriate for modeling the reaction time?

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