Question

What time must a student leave in the morning to be late 20% of the time if the time it takes to get to school follows a uniform distribution?

A) Leave at the median time
B) Leave at the mean time
C) Leave at the time corresponding to the 20th percentile
D) Leave at the time corresponding to the 80th percentile

Answer 1

To be late 20% of the time, a student must d. leave at the time corresponding to the 20th percentile in a uniform distribution.

Step-by-step explanation:

To determine what time a student must d. leave in the morning to be late 20% of the time, we need to consider the uniform distribution. In a uniform distribution, the probability of an event happening between two values is proportional to the length of the interval between those values.

In this case, we want to be in the late 20% of students. The 20th percentile corresponds to the time at which 20% of students are already at school and 80% are still on their way. Therefore, the answer is option C: leave at the time corresponding to the 20th percentile.