Normal approximation for at least 60 heads

Question

A fair coin is flipped $100$ times. Use the Central Limit Theorem, with no continuity correction, to approximate the probability of getting $60$ or more heads. Give the answer to five decimal places.

Short answer

About $0.02275$ . The head count has mean $50$ and standard deviation $5$ , so $60$ heads is two standard deviations above the mean, and $1-\Phi(2)\approx0.02275$ .

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Lessons behind this question

The Central Limit Theorem
Continuous Random Variables and Probability Density Functions
Cumulative Distribution Functions

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