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Answer :
Final answer:
We require both np and n(1-p) to be at least 10 for using a normal distribution to approximate binomial probabilities to ensure the shape of the binomial distribution is sufficiently similar to that of the normal distribution, which applies when np and nq are at least 5.
Explanation:
To understand why we require both np and n(1−p) to be at least 10 for using a normal distribution to approximate binomial probabilities, let's delve into the conditions behind this requirement. The binomial distribution describes the probability of having a certain number of successes in a fixed number of independent trials, each with the same probability of success (p). When the sample size is large enough (usually np ≥ 5 and nq ≥ 5), the shape of the binomial distribution begins to resemble the bell shape of the normal distribution.
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