The Cutoff Only 5% of Shifts Exceed

On a factory line, the time to assemble one unit is strongly right-skewed (most units are quick, a few jam badly). Across all units,

$\mu = 42.4 \text{ seconds}, \qquad \sigma = 12.6 \text{ seconds}$

Each shift, a supervisor times a random sample of $n = 49$ units and records the sample mean assembly time $\bar{x}$ for that shift.

She wants an alarm threshold $c$ such that only the slowest $5\%$ of shifts trigger it:

$P(\bar{x} > c) = 0.05$

Using the Central Limit Theorem, find $c$.

Take the standard normal critical value $z_{0.95} = 1.645$.

Round your answer to 2 decimal places.