You flip a fair coin 10,000 times. Approximate the probability that the difference between the number of heads and number of tails is at most 100.

The probability that the difference between the number of heads and number of tails is at most 100 is P=0.84375.

Step-by-step explanation:

Let X denote the amount of heads after 10,000 coin flips.

X will have a binomial distribution with p=0.5 and n=10,000.

When the difference between the number of heads and the number of tails is 100, thats when X=5,050: 5,050 heads and 4,950 tails.

We need to calculate the probability P(X≤5,050).

As the binomial distribution with such a large n is impractical, we use the approximation to normal

We use the continuity correction factor to make the approximation from the discrete variable to the continous variable.

The z-value is

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