A binomial experiment consists of 500 trials. The probability of success for each trial is 0.4. What is the probability of obtaining 190-205 successes? Approximate the probability using a normal distribution. (This binomial experiment easily passes the rule-of-thumb test for approximating a binomial distribution using a normal distribution, as you can check. When computing the probability, adjust the given interval by extending the range by 0.5 on each side.
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Step 1
Given: n = 500 (number of trials) p = 0.4 (probability of success) Mean (μ) = n * p = 500 * 0.4 = 200 Standard Deviation (σ) = sqrt(n * p * (1 - p)) = sqrt(500 * 0.4 * 0.6) = 10.95 Show more…
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