Answer in Statistics and Probability for Haley #247877

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

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

0.775

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?

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.

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