The mean is 17.8 and the standard deviation is 5.2. The shop does not want to give more than 1% of its customers free service, how long should the guarantee be? (cut the problem short, the rest was just story)
I think the equation I would use is X = Z(standard deviation) + Mean
The Attempt at a Solution
I changed 1% into the Z score and got -2.33 and plugged that into the equation, -2.33(5.2) + 17.8 and ended up with 5.684. That is lower than the mean though which does not make sense to me, why would the shop guarantee they can complete the job in 6 minutes (rounding up) is the mean is 17.8. Where did I go wrong? Thanks in advance!