Question 1191748
z-score formula is z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation
the mean is 200 minutes and the standard deviation is 10 minutes.


z-score for 180 minutes is (180 - 200) / 10 = -20/10 = -2.
if it's going to be at least 180 minutes, then you want the area to the right of that z-score.
the area to the left is equal to .02275, rounded to 5 decimal digits.
the area to the right is equal to 1 minus that = .97725.
that means the probability that the travel time will be greater than 180 minutes is 97.725%.



z-score for 205 minutes is (205 - 200) / 10 = .5
if it's going to be at most 205 minutes, then you want the area to the left of that z-score.
the area to the left is equal to .69146, rounded to 5 decimal places, 
that means 69.146% probability that the travel time will be less than 205 minutes.


here's a table that i normally use.
<a href = "https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf" target = "_blank">https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf</a>


the tables are designed to show you the area to the left.
the area to the right is equal to 1 minus the area to the left.