Question

The amount of time it takes Renee to go grocery shopping is continuous and uniformly distributed between 18.5 minutes and 40.5 minutes. What is the probability that it takes Renee at most 29 minutes to go grocery shopping

Answer 1

47.73% probability that it takes Renee at most 29 minutes to go grocery shopping

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 lower than x is given by the following formula.

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

Uniformly distributed between 18.5 minutes and 40.5 minutes.

This means that
`a = 18.5, b = 40.5`

What is the probability that it takes Renee at most 29 minutes to go grocery shopping

`P(X \leq 29) = (29 - 18.5)/(40.5 - 18.5) = 0.4773`

47.73% probability that it takes Renee at most 29 minutes to go grocery shopping