Little issue with Exercise 6.8.8

[vashcast]

The proposed solution is algebraically correct on the left hand side of the inequality of the first probability, but $\sigma$ stands for the standard deviation of the Poisson($\lambda=1$), which is $\sqrt{\lambda} =1$. This changes the rest of the solution as follows:

$\mathbb{P}\left(Y<90\right)=\mathbb{P}\left(\overline{X}_n<{90 \over n}\right)=\mathbb{P}\left(\sqrt{n}\frac{\left(\overline{X}_n-\mu\right)}{\sigma}<\sqrt{n}\frac{\left({90 \over n}-\mu\right)}{\sigma} \right) \approx \mathbb{P}\left( Z<\sqrt{100}\left({90 \over 100}-1\right) \right)= \Phi(-1)$.