The duration of Alzheimer’s disease from the time symptoms first appear until death ranges from 3 to 20 years; the average is 8 years with a standard deviation of 4 years. The administrator of a large medical center randomly selects the medical records of 30 deceased Alzheimer’s patients from the medical center’s database, and records the average duration. Find the approximate probabilities for these events:

1. The average duration is less than 7 years.

2. The average duration exceeds 7 years.

3. The average duration lies within 1 year of the population mean m =8.