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Geometric Random Variables

I need some help learning how to apply the normal approximation in this question:
Suppose that Yn for NB(n,p). Give a normal approximation for P(Yn<y) for large n.
Hint: Yn is distributed as the sum of n independent geometric random variables. Use the negative binomial distribution (see attached file for better formula representation).

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This solution contains step-by-step calculations on how to conduct a normal approximation for P(Yn<y) for a large n.

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