We appreciate your visit to For the following confirm that the normal distribution can be used to approximate the binomial distribution For each case clearly indicate the continuity correction and. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
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.
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