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QuestionStatistics
n the large counts condition to use a normal distribution to approximate binomial probabilities, why do we require that both np and n(1−p) be at least 10?
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Step 1I'll solve this problem step by step, explaining the reasoning behind the large counts condition for approximating binomial probabilities with a normal distribution.
Step 2: Understanding the Binomial Distribution
The binomial distribution models the number of successes in a fixed number of independent trials with two possible outcomes (success or failure).
Final Answer
The large counts condition (np \geq 10 and n(1 -p) \geq 10) ensures that the normal distribution provides a good approximation to the binomial distribution by guaranteeing: 1. Sufficient expected successes 2. Sufficient expected failures 3. Minimal skewness in the probability distribution This condition helps maintain the accuracy of probability calculations when using the normal distribution as an approximation.
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