# Normal and Poisson approsimation to binomial distribution

A fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A.

By using a suitable approximation to the binomial distribution, calculate the probability of A.

The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B.

By using another suitable approximation, calculate probability of B.

Also calculate the probability that B occurs exactly 3 times when 2000 such coins are each tossed 100 times on everyday of a given week.

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#### Solution Preview

Let X be the number of heads.

X ~ Bin (100, 0.5)

Since n=100 is large, p= 0.5 is not too small, such that

np = 50 >5 and nq = 50 >5

We use the normal approximation to binomial distribution

X ~N ...

#### Solution Summary

The solution addresses a fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A.

By using a suitable approximation to the binomial distribution, calculate the probability of A.

The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B.

By using another suitable approximation, calculate probability of B.

Also calculate the probability that B occurs exactly 3 times when 2000 such coins are each tossed 100 times on everyday of a given week.