= Solution
After $k$ measurements the <normal-normal conjugacy> formulas are
$$
v_{ik}=(\tau^{-2}+k\sigma_i^{-2})^{-1},\qquad
m_{ik}=v_{ik}\left(\mu\tau^{-2}+\sigma_i^{-2}\sum_{j=1}^k y_{ij}\right).
$$
The upper monitoring limit is $m_{ik}+z_{0.999}\sqrt{v_{ik}+\sigma_i^2}$. Its center moves toward the athlete's own mean and the population's influence diminishes. Its predictive width decreases toward $z_{0.999}\sigma_i$, since uncertainty about the mean vanishes but the next measurement's error remains. The absolute upper limit need not decrease monotonically: its center can move upward or downward with the observations. This is <sequential normal predictive monitoring>.
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