The rate of oxygen consumption for a specific species of deep-sea bacteria, measured in $\mu mol/h$, is normally distributed with mean $15.4$ and standard deviation $2.8$. A marine biologist collects a random sample of $n$ such bacteria. Determine the minimum sample size $n$ such that the probability of the sample mean oxygen consumption exceeding $16.5\mu mol/h$ is less than $1\%$.