The phrase "within the normal range" is correct and can be used in written English. You can use it to describe something that falls within the acceptable or expected limits for a particular measure or characteristic. For example, "The baby's weight was within the normal range for a newborn.".
I'm actually within the normal range.
But such adolescent slippages come within the normal range.
On exam, the patient's blood pressure was low, but well within the normal range.
She assured me that my ferritin was within the "normal" range.
My triglycerides, at 95, were well within the normal range of zero to 149.
All parameters were within the normal range.
Laboratory testing was within the normal range.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia