Solution
= Solution
Under the null, $Y$ has the <standard normal distribution>, so the <Type I error> is $\alpha=\mathbb P_0(Y>1.65)=1-\Phi(1.65)\simeq0.05$. Under the alternative, the <Type II error> is $\beta=\mathbb P_1(Y\leq1.65)=\Phi(1.65-2.49)=\Phi(-0.84)\simeq0.20$. Hence $\boxed{\alpha\simeq0.05,\quad\beta\simeq0.20}$, using the supplied rounded normal probabilities.