VAIO VGNTZ150N Laptop battery runs down when not...

Question

i have a laptop laptop that is about 6 months old. The battery runs down about 10% per day when the computer is off. I can charge it up completely and when i turn it back on 4-5 days later the battery is down to 50% or so. It does not run down if i remove the battery from the computer, the battery holds its charge when not installed in the computer. The life of the battery seems to be about 4-5 hours when fully charged and the laptop is in use on battery only so i think the laptop is using up the battery even when off. Is this normal?thanks