math
posted by Jessica on .
Express Courier Service has found that the delivery time for packages is normally distributed with mean 14 hours and standard deviation 2 hours. What should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered before this time? (Hint: note that 5% of the packages will be delivered at a time beyond the guarantee time period)

It would seem that you are only concerned with packages that would take longer than normal time to delivered. "Beyond" could infer either direction.
95% = mean + 1.645 SD
Insert value and solve.
If it were either direction:
95% = mean ± 1.96 SD