Answer to Question #247877 in Statistics and Probability for Haley

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.

What is the probability that on any given day, your travel time to class would be less than 20 minutes?

0.067

Correct: Your answer is correct.

What is the probability that on any given day, your travel time to class would be between 20 and 30 minutes?

0.775

Correct: Your answer is correct.

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?

Answer 1

To be late at most 1% of the time, the largest amount of time it takes to go to class should be less than 1% of all possible amounts. This amount corresponds to a z-score where 1% of the distribution is to the right of it. From the z-table or using technology, this z-score is 2.33.

z = (X - Mean)/Standard deviation = (X - 26)/4 = 2.33

X = 2.33(4) + 26 = 35.32 minutes

The largest amount of time I can spend to go to class is 35.23 minutes. This means I should leave the house the latest about 35.23 minutes before the class starts at 8 AM. Therefore, I should leave at around 7:25 AM.