Question

Suppose commute times in a large city are normally distributed and that 62.50% of commuters in this city take more than 21 minutes to commute one-way. if the standard deviation of such commutes is 6.2 minutes, what is the mean commute?

Answer 1

If 62.5% take more than 21 minutes 
37.5% take less than 21 minutes 

convert .375 to a zscore using the normal distribution chart in your book 

P(.375) = z -0.318639364 

(21 - x) / 6.2 = -0.318639364 

(21 - x) = -1.9755640568 

22.9755640568 = x 

mean commute is 22.98 minutes