Where the Rejection Region Starts

A support call centre's records show that the mean handling time of a call has historically been $\mu_0 = 240$ seconds, with a population standard deviation known exactly from years of logs: $\sigma = 30$ seconds.

A manager suspects calls are now taking longer, so she tests

$H_0: \mu = 240 \qquad \text{against} \qquad H_a: \mu > 240$

at significance level $\alpha = 0.05$, using a random sample of $n = 25$ calls.

She will reject $H_0$ whenever the sample mean $\bar{x}$ lands at or above a cutoff value measured in seconds. For a one-sided test at $\alpha = 0.05$, the critical value is $z^{*} = 1.645$.

What is that cutoff, in seconds? Round your answer to 2 decimal places.