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?Single choice
A
a. Geometric distribution
B
b. Uniform distribution
C
c. Poisson distribution
D
d. Binomial distribution

Question

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?Single choice

A

a. Geometric distribution

B

b. Uniform distribution

C

c. Poisson distribution

D

d. Binomial distribution

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?Single choice

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