Question

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 18 minutes and a maximum time of 34 minutes. what commute times represents the 40th percentile of this distribution?

Answer 1

24.4

Explanation:

To find the commute time that represents the 40th percentile of this uniform distribution, you can use the formula for percentiles in a continuous uniform distribution:

Percentile = Minimum + (Percentile Rank) × (Maximum - Minimum)

In this case, the minimum time is 18 minutes, the maximum time is 34 minutes, and you want to find the 40th percentile. Plug these values into the formula:

Percentile = 18 + (0.40) × (34 - 18)

Now, calculate the percentile:

Percentile = 18 + (0.40) × 16

Percentile = 18 + 6.4

Percentile = 24.4

So, the 40th percentile of this distribution represents a commute time of 24.4 minutes.