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A financial speculator identifies financial conditions which allows them to place an investment whose return will...

A financial speculator identifies financial conditions which allows them to place an investment whose return will be normally distributed with a mean return of 75,000 and a standard deviation of 10,000. Experience indicates that the number of times per year these specific conditions arise has a Poisson distribution with mean 2. Assuming that the financial conditions arise independently of one another and that the speculator places the investment each time it arises, find the probability that the speculator earns less than 80,000 in a year in total on their investment.

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