How do I use standard deviation to explain why 95% is acceptable?

Question

In this company, results are sent to customers within 2 working days. This is the target turnaround time. Below is the mean % of results sent out within the expected turnaround time for each year.

2019: 99.90%; 2020: 99.85%, 2021: 99.82%; 2022: 98.91%; 2023: 99.38%; 2024: 98.83%.

I worked out the overall mean is 99.45%. The overall standard deviation is 1.08%. How can I justify why a minimum of 95% results being sent out within the expected turnaround time is acceptable using this data?

I am just confused what I need to do to work this out? Normally I would used 1SD + mean, 2SD + mean, 3SD + mean. But this would give me values above 100%. Do I use SD below the mean instead? Even so, I don't know how to justify the 95%...

Appreciate any help!!

Answer 1

The same technique you mentioned works on the lower side of the mean as well as the upper.

For data that fits a normal curve:

1. 68.27% of all data lies between the (mean - 1 SD) and the (mean + 1 SD)
2. 95.45% of all data lies between the (mean - 2 SD) and the (mean + 2 SD)
3. 99.73% of all data lies between the (mean - 3 SD) and the (mean + 3 SD)
4. 99.99% of all data lies between the (mean - 4 SD) and the (mean + 4 SD)

Better check your calculations for standard deviation - I got a different value.