TLDR: You adjust the Apdex response times to suit your needs. You want response thresholds to be low enough to give you sufficient resolution of your system performance, without having it so low that you start receiving too many false alarms.
Here's what New Relic says about Apdex:
Apdex is a measure of response time based against a set threshold. It measures the ratio of satisfactory response times to unsatisfactory response times. The response time is measured from an asset request to completed delivery back to the requestor.
The application owner defines a response time threshold T. All responses handled in T or less time satisfy the user.
According to a Sales Engineer from New Relic, you should absolutely adjust the response time threshold T to suit your app. The biggest use for Apdex isn't so much the Apdex Score itself, but setting it up so the system can notify you during times of heavy usage so you can look into issues, and potentially scale up your servers to meet increase demands.
What should you set "T" to?
They recommend you monitor response times for ~ a week. Then look at your data to determine the average response time for "normal" usage. The "T threshold" should be set to be slightly above normal usage. This will give you maximum resolution for detecting issues with your system. However, you should be mindful that the lower the threshold, the more likely you are to receive false alarms. So set your threshold by balancing these two things.