Question

The amount of time it takes Ariana to do a math problem is continuous and uniformly distributed between 38 seconds and 79 seconds. What is the probability that it takes Ariana between 58 and 70 seconds to do a math problem

Answer 1

29.27% probability that it takes Ariana between 58 and 70 seconds to do a math problem

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d, d being greater than c, is given by the following formula:

`P(c \leq X \leq d) = (d-c)/(b-a)`

Uniformly distributed between 38 seconds and 79 seconds.

This means that
`a = 38, b = 79`

What is the probability that it takes Ariana between 58 and 70 seconds to do a math problem

`c = 58, d = 70`

`P(58 \leq X \leq 70) = (70 - 58)/(79 - 38) = 0.2927`

29.27% probability that it takes Ariana between 58 and 70 seconds to do a math problem