Answer :
Final answer:
Using the normal distribution to approximate the binomial distribution, we add or subtract 0.5 for continuity correction and compare the approximated probabilities with those from a binomial distribution table for various coin flip scenarios.
Explanation:
The subject in question involves using the normal distribution to approximate the binomial distribution. To confirm that the normal distribution can be used, the conditions np > 5 and nq > 5 need to be satisfied, where n is the number of trials, p is the probability of success, and q = 1 - p. The continuity correction is used by adding or subtracting 0.5 to the discrete x value when approximating a binomial with a normal distribution. The student is asked to calculate probabilities in different scenarios of flipping a coin 20 times.
Calculations for Each Scenario
- For 10 to 15 heads, the normal approximation would be used with continuity correction. The mean (μ) is np and the standard deviation (σ) is √npq. The probabilities from the normal distribution and binomial distribution tables would be compared.
- For at least 15 heads, similar steps are followed as above but considering the correct continuity correction (x + 0.5).
- For fewer than 6 heads, the calculation would use a continuity correction of (x - 0.5).
Ultimately, the probabilities calculated via the normal approximation will be compared to those from the binomial distribution table.
Learn more about Normal Approximation to the Binomial Distribution here:
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