Relatively basic question here ..
A Company wants to give gifts to the top 5% of customers. If the mean spend per customer is $ 135 - with a standard deviation of 55 - what balance should the company specify?
However, at the end of the first month it was found that 8% of customers qualified for the free gift. What has happened? Assuming that the standard deviation hasn’t changed, calculate the new mean spend per customer.
HOW do I calculate the Z Score for these questions ?
The first part of the question's z score = 1.645 which makes sense if looking at the z-table.
But according to the answer for the second part of the question the z score = 1.405. This I do not understand -- the closest percent on the z-table is 0.9207 with a z-score of 1.401 -- How do they calculate this ? and why is the closest percentile to 92% on the z-table not used ?