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If in Binomial distribution \( n=5, p=0.2, q=0.8 \) then we can approximate it to normally disputation

Ask by Garrett Peters. in Saudi Arabia
Mar 10,2025

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The binomial distribution with \( n=5 \), \( p=0.2 \), and \( q=0.8 \) cannot be approximated by a normal distribution because both \( np \) and \( nq \) are less than 5.

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When you have a Binomial distribution with parameters \( n=5 \) and \( p=0.2 \), you calculate the mean (μ) as \( np = 5 \times 0.2 = 1 \) and variance (σ²) as \( npq = 5 \times 0.2 \times 0.8 = 0.8 \). However, for a good normal approximation, both \( np \) and \( nq \) should be greater than 5, which isn't the case here. This means that while you could technically attempt to use the normal approximation, the distribution remains skewed and might not yield accurate results. In practice, when working with small sample sizes like this, it's often better to rely on the exact probabilities calculated from the binomial formula rather than approximating to a normal distribution. So, stick to the binomial distribution for better accuracy!

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