How Often Would It Catch the Effect?

A chemical plant tests whether a new catalyst raises the mean yield per batch. Yields are normally distributed and the population standard deviation is known: $\sigma = 20$ kg.

The test is

$H_0: \mu = 60 \qquad \text{against} \qquad H_a: \mu > 60$

run at $\alpha = 0.05$ on a random sample of $n = 25$ batches. The one-sided critical value is $z^{*} = 1.645$.

Now suppose the catalyst genuinely works, and the true mean yield is $\mu = 70$ kg.

Standard normal CDF values $\Phi(z) = P(Z \le z)$, for reference — most of these rows are not needed:

What is the power of this test against $\mu = 70$ kg? Give the power as a decimal (not a percentage), rounded to 3 decimal places.