Normal Distribution

Question

Sometimes we can model the binomial distribution using the normal distribution if the number of trials is large enough. Use this to answer the following question: If I flip a coin 300 times, what is the probability I get between 120 to 160 heads?

Answer 1

Number of trials (n): 300

Probability of success (p): 0.5 (since it is a fair coin)

Probability of failure (q): 1 − p = 0.5

Mean (μ): n × p = 150

Standard deviation (σ): √n×p×q = 8.66

Then, use these parameters for the Normal distribution. In other words, this now turns into a Normal distribution problem. Using a TI-84, the input would be normalcdf(120, 160, 150, 8.66)

The answer you get should be approximately 0.8869

Hope this was helpful.