Question: > 
> Theorem:
> 
> 
> Let M be a topological manifold and let U be any open subset of M, with the subspace topology. Then U is a topological manifold.
> 
> 
> 

Now, the only problem I face is showing that U is locally euclidean.

> 
> Recall: Locally euclidean
> 
> 
> A topological space U is locally euclidean if, $\exists n \in \mathbb{Z}^{+}, \forall \bar{u} \in U$, there exists an open set $\alpha \subseteq U$ containing $\bar{u}$ homeomorphic to some open set $\beta \subseteq \mathbb{R}^{n}$
> 
> 
> 

Any help is appreciated.

Answer: 
(y-np+0.5 #continuous correction
)/(npq^1/2)
<(9.5-7.5)/2.5
=0.8 

so
result is Pr(Y>9.5)=1-Φ（0.8）＝1-0.788=0.212
Hints:

* Let $X$ denote the lifetime of a component. Then:$$X<900\iff 0.01X-10<-1$$
What can be said about the distribution of $0.01X-10$?
* Of $45$ components let $Y$ denote the number of components having a lifetime less than $900$. Then $Y$ has binomial distribution with parameters $n=45$ and $p=\Pr(X<900)$.