Question

Bob 's daily commute time is randomly distributed with a minimum of 20 minutes, a maximum of 61 minutes, and the most common length is 30 minutes. What is the probability that his commute today took more than 35 minutes?

Answer 1

The probability that Bob's commute took more than 35 minutes is roughly 63.41%, calculated using the formula for a uniform distribution.

Step-by-step explanation:

The probability of a scenario within a uniformly distributed dataset can be determined by calculating the proportion of the data range that meets the criteria. In Bob's case, his commute time is uniformly distributed between 20 minutes and 61 minutes. We want to find out the probability that his commute took more than 35 minutes.

To calculate this probability, we subtract the lower time limit (in this case, 35 minutes) from the maximum time (61 minutes) and divide by the total range of commute times (61 minutes - 20 minutes).

Using the formula Probability = (Max - Lower Limit) / (Max - Min), we have:

Probability > 35 minutes = (61 - 35) / (61 - 20)

Probability > 35 minutes = 26 / 41

This simplifies to a probability of approximately 0.6341, meaning there is roughly 63.41% chance that Bob's commute time will be more than 35 minutes.

Answer 2

0.6341 = 63.41% probability that his commute today took more than 35 minutes

Step-by-step explanation:

Randomly distributed = Uniform distribution.

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

`P(X > x) = (b - x)/(b - a)`

Randomly distributed with a minimum of 20 minutes, a maximum of 61 minutes.

This means that
`a = 20, b = 61`.

What is the probability that his commute today took more than 35 minutes?

`P(X > 35) = (61 - 35)/(61 - 20) = 0.6341`

0.6341 = 63.41% probability that his commute today took more than 35 minutes