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Poisson approximation to binomial distribution

In a large town, one person in 80, on the average, has blood of type X.

a)If 200 blood donors are taken at random, find an approximation to the probability that they include at least five persons having blood of type X.

b)How many donors must be taken at random in order that the probability of including at least one donor of type X shall be 0.9 or more?

Solution Preview

a) Let X be the number of blood donors of type X, where X~Bin(200, 1/80)

Since n=200 is large, p=1/80 is small such that ...

Solution Summary

In a large town, one person in 80, on the average, has blood of type X.

a)If 200 blood donors are taken at random, find an approximation to the probability that they include at least five persons having blood of type X.

b)How many donors must be taken at random in order that the probability of including at least one donor of type X shall be 0.9 or more?

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