Question

You have an 8:00 a.m. class and based on your experience, you believe the amount of time it takes you to travel from your home to your seat in the classroom follows a normal distribution with mean 26 minutes and standard deviation 4 minutes.

Then, you have no desire to be late to class, but neither do you want to leave the house every day at 6:00 a.m. for your 8 o'clock class. You are willing to risk being late to class 1% of the time, and the question is what is the latest time you can leave the house to have no more than a 1% probability of being late to class?

Same question if you are willing to risk a 5% probability of being late.

Answer 1

It is given that the amount of time it takes you to travel from your home to your seat in the classroom follows a normal distribution with mean 26 minutes and standard deviation 4 minutes. Hence .

We need the time taken to the class  to be less than 1% of the time. Then

So you should start at least 35.31 minutes before 8 AM. You should start at .

We need the time taken to the class  to be less than 5% of the time. Then

So you should start at least 32.58 minutes before 8 AM. You should start at .